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• Theoretical model of the double tumbler is built to derive the equation of motion. • The eigenmodes of double tumblers are synchronous and bidirectional swings. • Motion of double tumblers is periodic or quasi-periodic under various excitations. • Two adjacent resonance peaks shows great potential for broadband absorbers. The oscillation mechanism of tumblers differs from traditional mass-spring-dampers. This work studies the complicated dynamic behaviors of a double tumbler on a curved surface. The theoretical model of the double tumbler is established, and the equations of motion based on the Lagrange equation are derived. The effects of the geometric parameters on the dynamic responses are analyzed numerically. The experiment is also conducted to validate the theoretical model of double tumblers. The results show that two eigenmodes of the double tumbler are the synchronous and bidirectional swings, respectively. Due to the amplification effect of double tumblers on the dynamic responses, the amplitudes of the inner tumbler are larger than that of the outer tumbler. The resonance peaks and the peak frequencies of the swing angles can be changed significantly by adjusting geometric parameters. In addition, the double tumblers can exhibit periodic and quasi-periodic oscillations with the increase in the excitation amplitude. The unique dynamic characteristics of the double tumblers show great potential for the design and application of low-frequency devices, such as absorbers and energy harvesters. [ABSTRACT FROM AUTHOR]

• A parametrically excited energy harvester with a resonant attachment is proposed. • Interactions with the attachment expanded the harvesting frequency range. • Intentionally introduced perturbations facilitated entry into the unstable region. • Resonant energy transfer rapidly induced a high-amplitude steady-state response. Drawing inspiration from the enhancement of sensing capabilities in Micro-electro-Mechanical Systems (MEMS), the utilization of parametric resonance with nonlinear amplification features shows promise in vibration energy harvesting. However, harnessing parametric resonance for vibration energy harvesting presents several challenges. Initiating the resonant regime under low-energy conditions can be challenging, and the periodic modulation of system parameters requires additional time to accumulate the vibration amplitude. The range of modulation frequencies needs to trigger parametric resonance is notably narrow, especially when employing piezoelectric transducers for energy harvesting. To address these concerns, a parametrically excited piezoelectric energy harvester incorporating with a movable resonant attachment is proposed. The governing equations of this system were derived using the extended Hamilton principle and then numerically solved. Experimental testing was performed based on the design, and it displayed good agreement with numerical predictions. System parametric studies were carried out, revealing the mutual influence among critical system parameters. The findings demonstrate that the proposed device exhibited hardening dynamic responses and achieved more than a fivefold increase in overall bandwidth compared to a conventional parametrically excited counterpart. [ABSTRACT FROM AUTHOR]

• The electromagnetic launch rail-structure is modeled as beam on elastic foundation. • The finite element model is proposed to study the dynamic response of rail-beam. • The beam dynamics is analyzed subjected to the extended moving load. • More precise load amplitude for the extended moving load is confirmed. • The dynamic difference for rail vibration under various moving loads is revealed. The distributed load with loaded area being extended over the whole structure (i.e., the extended moving load) that occurs during the operation of an electromagnetic launch rail-structure, is different from loading cases studied previously such as the concentrated load or distributed load on a finite segment (i.e., the single moving load), or a series of single moving loads in a periodic pattern (i.e., the periodic moving load). In this paper, a nonlinear finite element model is proposed by modeling the rail-structure as a Euler-Bernoulli based beam on an elastic foundation to study the dynamics of rail-beam under such an extended moving load. The proposed model is firstly verified by comparison with the analytical solution for the rail-vibration response under the extended moving load at constant speed, and the model feasibility is further revealed by comparison with the experimental results of rail strain. The significant differences of rail vibration modes are observed between the extended moving load and the single, or periodic moving load. Moreover, the maximum error of the middle of the rail between the linear forcing and nonlinear forcing will decrease with the increase in the foundation elastic modulus, but increases with the increase in the pulse current. Those results will improve our understanding on dynamics of beam under the more comprehensive loading cases. [ABSTRACT FROM AUTHOR]

• A breathing crack model based on fracture mechanics theory. • A proposed time-varying integration method better simulates the practical process of crack opening and closing. • The breathing effect of cracks induces strong nonlinearities in the radial and torsional responses. • Radial-bending and bending-torsional combined vibrations induced by crack breathing effect. Rotor failures due to cracked blades are frequently observed in rotating machinery. The identification of cracking state of rotating blade based on vibration characteristics has garnered a lot of attention. However, nonlinear characteristics and vibration combining in radial, bending and torsional directions of a rotating blade induced by the crack breathing is yet not clear. This paper proposes a radial-bending-torsional dynamic model of rotating blade with breathing crack. A time-varying integration method is proposed for determining the crack state based on the strain energy release rate. The crack breathing behavior is described by Boolean operation and the numerical integration are applied to open or close the crack. The model is validated through modal analysis, vibration responses and contact state of crack surface. Frequency veering is changed between the 2nd flap and 1st edgewise frequency due to the existence of crack. Strong nonlinear behaviors are found in the radial and torsional vibrations because of the crack breathing. Nonlinearities are also found in the combined vibrations between the radial-bending and the bending-torsional directions. Radial and torsional vibration amplitude levels can be used as an indication of blade crack failure, but the applicability depends on the absolute response decided by the aerodynamic excitation and resonant vibration. These findings can serve as guidance in crack identification and cracking state monitoring of rotating blades. [ABSTRACT FROM AUTHOR]

• Improvement of dynamic performance by actuation of piezoelectric top foil. • Suppression of sub-synchronous frequencies by optimal placement of PZT patches. • Increasing onset of instability speed for both single and three pad bearings. • Necessity of order reduction method to find the optimized configuration. It is well documented that the static and dynamic performance of foil air bearings (FABs) can be improved through the alteration of the radial clearance profile. One way of achieving such controllability is through piezoelectric actuation of the top foil. Such a piezoelectric foil air bearing (PFAB) avoids the dynamics complications introduced by alternative actuating mechanisms. So far, theoretical analysis of a PFAB pad in isolation has shown that top foil actuation can raise the static load capacity. This paper theoretically investigates the potential for improving the dynamic performance. A computational approach that uses Galerkin Reduction (GR) to model the air film and considers the detachment of the top foil from the bump foil is upgraded for multi-pad PFABs, thus facilitating parameter optimization. The investigation considers two conventional FAB rotor systems from the literature that exhibit strong sub-synchronous vibrations under high unbalance. It is found that the optimal voltage and placement of piezoelectric patches can result in total suppression of the strong sub-synchronous frequencies, as well as a rise in the onset of instability speed. The polarity of the voltage required for suppression of the sub-synchronous frequencies is found to be opposite to that required to raise the load capacity. [ABSTRACT FROM AUTHOR]

• The study proposed a method to predict the complex subharmonic vibrations. • Local subharmonic vibrations of order-1/3 and −1/5 were obtained accurately. • Local "full tree" and "half tree" of subharmonic vibrations were predicted. • Strange vibrations in the real turbo-engine testings were explained. • Experiments were conducted for comparing with the theoretical predictions. In real turbomachinery testing, we always confront strange high order vibrations which scatter a few points or draw some local lines in the experimental bifurcation diagrams. Such vibrations maybe ignored due to the lack of experiences and knowledge while they can be important in design and operation due to the nonsmooth jumping and instability. This paper proposes a new method for predicting the complex high order subharmonic vibrations for a nonlinear rotor system with light rub. The nonlinearity is induced by the contact of the bristles and the rotor. A continuous nonlinear rotor system is established based on the geometric and bending force diagrams. We discretize the complex orbits and built implicit mappings between the adjacent nodes. A directional eigenfunctional matrix is constructed which maps each nodes and passes the perturbation along the orbits for semi-analytical prediction of the high order subharmonic vibrations. Stability criterion is defined. Numerical bifurcation diagrams and harmonic contours are presented for quick glance of the global subahrmonic vibrations. Two local subharmonic vibrations of odd orders are succesfuly predicted. Local high order subharmonic vibrations of "full tree" and "half tree" are predicted and achieved accurately. An experimental platform is established to compare the semi-analytical predictions with experimental results. The research delivers a new perspective for predicting and computing the high order subharmonic vibrations in nonlinear rotor system. [Display omitted] [ABSTRACT FROM AUTHOR]

• The nonlinear dynamic models of riser under different suspension evacuation conditions are established. • The nonlinearity of the model takes into account the actual configuration of riser, VIV in cross-flow (CF) and in-line (IL) directions, and large deformation. • Experiments are designed and carried out to verify the nonlinear model. • The vibration frequency and mode shape of riser under different influence factors are analyzed. This paper establishes a nonlinear dynamic model for a suspended riser under the condition of considering realistic configurations, based on the principles of virtual work and Hamilton's variational principle. The nonlinearity of the model is manifested by considering vortex-induced vibration in the cross flow (CF) and in-line (IL) directions, as well as large deformations, taking into account the variable diameter of the riser in the compliant riser system. The model is discretized using the finite element method and solved using the Newmark-β method. Experimental validation is conducted to verify the effectiveness of the model. Utilizing the parameters of a riser in a well in the South China Sea, the paper explores the influence of different environmental and structural parameters on the VIV response characteristics of a compliant riser. Results show that the vibration frequency is controlled by both the bare tube and buoyant block when the buoyant block coverage rate is 25%, which can significantly inhibit VIV. With the increase of flow velocity, the VIV energy jumps from low order to high order, and the riser mode also transitions from low order to high order. The increase in suspension length transfers the vibration energy from high to low frequency, thus realizing energy transition and mode shape transformation. With the increase in LMRP weight, the vibration and natural frequencies of the riser increase synchronously, the vibration amplitude decreases, and the mode shape remains unchanged. [ABSTRACT FROM AUTHOR]

• The nonlinear vibration analysis approach of high-speed and ultra-precision mechanism with clearance joints is proposed. • The prediction of motion reliability is conducted by the kinematics trajectory. • The phase portrait and probability density distribution are employed to evaluate the periodicity and chaotic. The main purpose of this study is to present a comprehensive approach to illustrate the dynamic behavior of ultra-precision mechanism with clearance joints. According to geometrical features, the Largrange's equations of this mechanism is established. In order to describe the contact-impact process accurately, the models of dissipative contact force and modified friction force are introduced into the dynamic analysis model of this mechanism with clearance joints, which could describe the vibration characteristics clearly. Moreover, the experimental performance platform of high-speed and ultra-precision mechanism is designed and built. Then, the dynamic response of this mechanism is represented with the simulation and experiment, which demonstrates the effectiveness of proposed model. In addition, the probability statistics, largest Lyapunov exponent and bifurcation characteristics are employed to study the effects of clearance joints on the dynamic behavior of this mechanism. [ABSTRACT FROM AUTHOR]

• Constructing fractional-order foundation model for hydrogenerator unit. • Deriving nonlinear broadband dynamic equations for CSFS. • Discussing differences between CSFS and traditional single shaft system. • Analyzing the coupled dynamic performances of CSFS. The analysis of the coupled shaft-foundation system (CSFS) of a water turbine generator set is an extremely complicated task owing to its structural complexity and inherent nonlinear broadband dynamic characteristics. Thus, the coupling relationships of the CSFS remain unclear. The broadband vibration of the foundation subsystem has an evident influence on the vibration of the shaft subsystem of the unit; however, for the analysis of the dynamic characteristics of the water turbine generator, an overly complicated foundation can be reasonably simplified. To this end, this paper reports the development of novel energy-equivalent broadband modeling approaches to investigate the nonlinear vibration characteristics of CSFS. First, a relatively traditional integer-order lumped parameter model of the foundation subsystem was constructed, and its parameters were determined by fitting the response spectra obtained from an accurate hydropower house model. To improve the narrow-frequency limitation of the integer-order model and account for random disturbances, a novel fractional-order broadband modeling method is proposed. The advantage of the proposed fractional-order equivalent foundation model is that it can simultaneously reveal the broadband characteristics of complex structures at low frequencies of less than 1 Hz to high frequencies of hundreds of Hz with a single degree of freedom. Finally, coupled dynamic equations for the fractional-order CSFS model were derived and solved by considering the actions of various nonlinear factors and hydraulic pulsation excitation. A comparison of the dynamic responses of the CSFS with field test data demonstrated the effectiveness and practicability of the proposed modeling approaches. The results of the integer- and fractional-order CSFS models provide insights into the abundant dynamic laws and inner mechanisms of the nonlinear coupled dynamic system. Furthermore, they provided a reliable theory for the design and stability analysis of a hydropower unit, considering the varied vibrations of the coupled foundation. [ABSTRACT FROM AUTHOR]

Negative stiffness vibration isolation devices have attracted significant attention and research interest for their ability to enhance the low-frequency vibration isolation performance of passive vibration isolators. However, their narrow linear negative stiffness region has hindered their broader application. To address this limitation, a novel design method for vibration isolators is proposed, integrating the permanent magnetic negative stiffness device (NSD) with the displacement amplification mechanism (DAM). The paper begins by presenting a specific vibration isolator design method and analyzing the kinematic relationship. Next, a single-degree-of-freedom (SDOF) nonlinear equivalent model of the vibration isolator is established using the pseudo-rigid-body model (PRBM) approach. Numerical simulations are then conducted to obtain the transmissibility of the isolator. Furthermore, two isolators—one with the displacement amplification effect and another without—are manufactured, and experimental investigations are carried out. The experimental results confirm that the incorporation of the displacement amplification mechanism effectively expands the linear negative stiffness region of the negative stiffness magnet pair, enabling wide-frequency and large-amplitude vibration isolation. Notably, these experimental findings align well with the simulation results. In summary, this paper proposes a creative design method for wide frequency and large amplitude vibration isolators, and proves it through theoretical analysis and experimental validation. • A create negative stiffness isolator based on displacement amplification is proposed. • The linear region of the negative stiffness is significantly expanded by three times. • Employ the harmonic balance method for nonlinear equation solving and simulating. • Inspire the design of large displacement amplitude negative stiffness isolators. [ABSTRACT FROM AUTHOR]

• Tapered composite structures are used in helicopter yokes, flexbeams, blades, etc. • FEM using tapered plate elements is employed for nonlinear free vibration analysis. • Newton–Raphson scheme with Newmark integration is used to obtain the time response. • Influence of ply-layup, anisotropy, end conditions, and aspect ratio are studied. • Tapered composite structures exhibit more hardening nonlinearity than uniform ones. Thickness-tapering in multi-layered composites is achieved by terminating the plies at discrete locations. This allows for effective material utilization and significant weight savings and is adopted in applications involving multi-layered composites that demand variation in thickness such as helicopter yokes, flexbeams and rotor blades, aircraft wing-skin structures and turbine blades. In the present work, the nonlinear free vibration of such tapered composites undergoing moderately large deflections is investigated for the first time. A general nonlinear finite element formulation for tapered multi-layered composite plates based on Reddy's higher-order shear deformation theory and considering Von Karman nonlinearity is developed. Newton–Raphson scheme in conjunction with Newmark time-integration technique is employed to obtain the time response. The developed model is validated against available results in the literature and through experimentally obtained linear natural frequencies of a honeycomb sandwich plate with tapered face sheets. Parametric studies are conducted to deeply understand the nonlinear dynamic behaviour of tapered composite structures. The investigation reveals that tapered multi-layered composite plates exhibit higher nonlinearity compared to uniform plates thus necessitating the consideration of nonlinear effects in the analysis of such structures. [ABSTRACT FROM AUTHOR]

The self-synchronization of rotors in a nonlinear system has both academic and practical importance because of its applicability as a source of excitation for vibratory machines. Although the characteristics of such self-synchronization can be clarified by analyzing the periodic solutions of the equations of motion, only self-synchronization corresponding to the stable periodic solution is realized in actual systems. The stability of the solution is thus one of the most important characteristics of self-synchronization. In this paper, to stabilize periodic solutions suitable for application to vibratory machines, the effects of the damping of the rigid body and the moment of inertia of the rotors on stability are examined using a system that consists of two unbalanced rotors installed in a rigid body. High-precision analysis conducted using the shooting method shows that it is possible to stabilize the instabilities caused by period-doubling and Hopf bifurcations while keeping other characteristics, such as the synchronous frequency and the rigid body amplitude, mostly unchanged. The findings of this study can serve as a guide to extending the range of stable periodic solutions and are thus expected to be useful in the design of systems that utilize the self-synchronization of rotors. [ABSTRACT FROM AUTHOR]

• This study investigated the energy harvesting potential of a magneto-electric and fluid-structure interaction system, where a magnet repulsive force was applied on a PZT located at a nonlinear beam. • The magnet repulsive force significantly enhanced the electric generation capability of the system. Specifically, when the PZT was positioned at the curved area of the pipe, the energy generation increased by 193.197 % compared to the system without a magnet. • To ensure optimal energy conversion, it is important to accurately estimate the frequency of parametric resonance in the flow-induced vibration system and ensure that the energy harvesting system operates within that frequency range. This research proposes an innovative design of a fluid-solid coupling vibration energy harvesting system (VEH system) that includes a downstream waterwheel driven by the flow field, which, in turn, drives gears and connecting rods to rotate a wheel equipped with magnets to generate electricity by changing the magnetic field. A piezoelectric patch (PZT) is installed upstream of the pipeline with a magnet attached to it. The repulsive force between the magnet on the wheel and the magnet on the PZT generates additional force while also creating vibration through fluid-solid coupling of the pipeline. The study derives a theoretical model of the nonlinear vibrating beam and couples it with the piezoelectric and magneto-electric equations to simulate the vibration of the fixed-fixed elastic pipe. The method of multiple scales (MOMS), fixed points plots, phase plots, and Poincaré maps are employed to verify the theoretically predicted parametric excitation properties of the system. The study uses the Biot-Savart Law to calculate the theoretical magnetic force and combines it with the fluid-conveying nonlinear beam and the PZT to create a magneto-electric coupling fluid pipeline vibration energy harvesting model. The study conducts a simple experiment to verify the feasibility of the theoretical model and demonstrates that the repulsive force of the magnet significantly enhances the electric generation benefit of the system. Regardless of whether the PZT is located in the curved or flat area (straight part) of the nonlinear beam, the addition of magnets to the system significantly increases voltage generation efficiency by more than 190 % when compared to systems without magnets. [ABSTRACT FROM AUTHOR]

• A theoretical model of the 2DOF-suspender considered the coupling effect of the first three modes has been developed. • The multimodal coupling effect leads to non-planar modal and planar/non-planar multimodal internal resonance. • The strength of multimodal coupling effect determines the contribution of lower and higher order modal responses. The objective of this paper was to investigate the 2-DOF suspender response under the condition of vortex-induced force and reveal the multimodal coupling mechanism. Firstly, an elastically mounted segmental model of suspender was established. Wind tunnel experiments were conducted to obtain the time history displacement signals in cross-flow and in-line directions, the empirical parameters were obtained by identify those signals. The nonlinear partial differential motion equation of suspender with two degrees of freedom was established based on Hamilton's principle, which considered the dynamic strain, bending stiffness and vortex-induced force of suspender. The Galerkin method was used to discretize the nonlinear partial differential equations into nonlinear motion governing equations, which considered the first three order modes. A numerical method was used to solve the motion governing equation, the time history displacement curve, phase diagram, amplitude spectrum and Poincare map of the multi-modal responses in the cross-flow and in-line directions were obtained. With the weak coupling effect of nonlinear stiffness and vortex-induced force, the cross-flow and in-line responses demonstrate period doubling bifurcation, quasi-periodic vibration, period doubling vibration, crises and transient chaotic phenomena. However, with the strong coupling effect, the crises and transient chaos in response amplitude disappear. More importantly, planar/non-planar multimodal internal resonance were found in this work. With the weak multimodal coupling effect in suspender response, the low-order modal response is dominant; as the multimodal coupling effect increases, the high-order modal response becomes predominant. In addition, the system energy not only transfers from high-order modal response to low-order modal response, but also the system energy transfer from low-order modal response to high-order modal response. These conclusions are useful for the design and practical engineering of suspenders, which have high theoretical research value in understanding the mechanism of multimodal coupling effects on suspender response. [ABSTRACT FROM AUTHOR]

• A new strategy is proposed for vibration control of flexible pendulums. • We introduce a flywheel to control flexible pendulum vibration. • The control method has robustness and is effective for nonlinear forced vibration. • An experiment platform is built to validate the proposed control strategy. Flexible inverted pendulums have found wide applications in mechanical systems, but their stability is susceptible to external disturbances. In this study, a new strategy that employs a flywheel to suppress vibration of flexible inverted pendulums is proposed. We develop the theoretical dynamic model of flexible pendulums with a flywheel by the Euler-Bernoulli beam theory, where the axial displacement of the pendulum and geometric nonlinearities are considered. An active control method based on the Bézier trajectory is proposed, where the acceleration of the flywheel is set as the input. Additionally, the equivalent damping ratio of the system including flywheel's motion is derived. The relationship between the parameters in the control equation and the suppression effect is obtained through the simulation of the equivalent damping ratio. Then, an experimental platform is built. The experimental results show that the present control strategy has good suppression effect on the vibration of the flexible inverted pendulums when selecting appropriate parameters. Meanwhile, the results of anti-disturbance test show that the present method has a certain robustness. Finally, the simulation results show that this strategy is also effective for nonlinear forced vibration under different excitation frequencies. [ABSTRACT FROM AUTHOR]

The pursuit of novel, environmentally friendly solutions for mobility and transportation has been a relevant area of technical and scientific progress in recent years. In this regard, the Hyperloop concept is a novel solution for sustainable transportation of people and goods at high speed. The electrodynamic levitation system in Hyperloop represents a key enabling technology. Nevertheless, its unstable nature is crucial and requires proper analysis and understanding. This paper proposes the experimental stabilization of electrodynamic maglev systems by means of passive components. A downscaled test setup is used to validate the numerical models that govern passive maglev systems. Setups for quasi-static and dynamic testing are proposed. The former experiments lead to model parameter tuning. The latter reproduce unstable behavior and assist in testing a stabilization method. Results in the time and frequency domains are used to analyze the system response and validate the proposed approach. • Electrodynamic levitation enables ultra-high-speed maglev transportation. • We propose a model to capture the instability of electrodynamic systems. • A test bench is developed to validate the proposed model. • Maglev stabilization is proposed and tested through experiments. • The numerical model matches the experiments in the frequency domain. [ABSTRACT FROM AUTHOR]

Shimmy dampers are passive solutions for undesired shimmy vibration in aircraft landing gears. Although they mitigate shimmy to variable degrees, they can introduce weight, cost, and reliability penalties especially when added to existing landing gear systems. More effective and compact shimmy dampers with reduced maintenance effort and enhanced stability performance can then greatly contribute to light-weighting, as well as lowering the aviation risk and maintenance costs. Moreover, a robust performance analysis and characterization framework based on high-fidelity computational models is absent from the literature while it is essential to quantify the capabilities of a given damper. In this work, analysis of a novel shimmy damper concept is presented along with an effective methodology for evaluating the performance of shimmy dampers based on nonlinear shimmy amplitude maps and stability boundary plots. The new damper concept is suitable for installation on existing and new landing gears and features a multifunctional torque link member including an assembly of beam and damping units to suppress the undesired vibrations. The influence of torque link damper parameters is then thoroughly explored using the nonlinear Multibody Dynamics model of the nose landing gear employed for both generating the shimmy maps and time histories of the vibrations. The novel concept is shown to be capable of effectively mitigating the rotational shimmy given that the parameters are chosen appropriately based on the systematic approach laid out. The insights from the analysis are then distilled in the form of recommendation for designing next generation shimmy dampers. Moreover, the novel framework introduced for characterizing shimmy dampers offers great benefit to the shimmy suppression research and development practice. [ABSTRACT FROM AUTHOR]

This paper presents a numerical method for analyzing the nonlinear structural and acoustic responses of a coupled stiffened composite laminated cylindrical shell and piecewise isolation system immersed in an infinite acoustic fluid. The cylindrical shell is reinforced by a series of circumferential rings and longitudinal stringers, which may be few or many in number, non-uniform or uniform in size, and arbitrarily distributed in space. The isolation system in the shell contains motion-limiting stops, and the restoring forces of the isolators are assumed as bi-linear functions of the isolator deformations. A modified variational approach for the shell combined with a discrete element method for the rings and the stringers is employed to establish the nonlinear dynamics model of the structural system. The exterior acoustic fluid is computed by a time-domain Kirchhoff boundary integral formulation. The structural and acoustic models are coupled together by considering the compatibility conditions on their interface. The validity of the present method for predicting the structural and acoustic responses of the coupled shell and isolator system is confirmed. The contribution of the grouped circumferential wave modes of the shell to the vibration and radiated sound of the coupled structural system is examined. The effects of the excitation frequency of the external load, as well as the stiffness ratio and the gap of the suspension springs in each isolator on the structural and acoustic responses of the coupled system are discussed. [ABSTRACT FROM AUTHOR]

Abstract This paper presents experiments and numerical simulations of a nonlinear rubber isolator subjected to both harmonic and broadband random excitations. Harmonic and broadband random excitations are performed experimentally in order to show the softening effect of the rubber isolator for high amplitudes of displacement and to show the temperature dependency of its mechanical properties. Firstly, the rubber isolator is modeled as a one degree-of-freedom system, whose stiffness and damping depend only on the amplitude of the relative displacement of the joint. The relationship between the stiffness and the damping versus the amplitude of the relative displacement of the rubber isolator is updated via experiments. Secondly, the Harmonic Balance Method (HBM) and the shooting method are presented and extended to take into account both harmonic and random excitations. A modification of the nonlinear methods is necessary in order to recover the information concerning the displacement amplitude. Moreover, for random excitations, a periodogram strategy is used to ensure a good estimate of the resulting Power Spectral Density (PSD). Finally, comparisons between experiments and simulations are undertaken. Good correlations are observed for harmonic and broadband random excitations, thus validating the modeling of the rubber isolator and the proposed nonlinear methodology. Highlights • Harmonic Balance Method (HBM) and shooting method for mechanical systems with stochastic excitations. • Application for a rubber isolator subjected to harmonic and random vibrations. • Comparisons between experiments and numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract A nonlinear energy sink (NES) is a promising device to reduce structural vibrations. If a nonlinear energy sink moves vertically, in principle, its weight cannot be ignored together with the initial deformation due to the static equilibrium. The present work investigates dynamic effects of the weight on the vibration of a structure coupled with a nonlinear energy sink, which is modeled as a 2-degree-of-freedom system. Free vibration is numerically examined. Forced vibration is analytically explored via the method of harmonic balance with numerical validations. It is found that the freely vibrating frequency is larger than the natural frequency of the structure except for an unreasonably small NES mass if the weight is considered, while it is smaller if the weight is ignored. It is also found that the steady-state response of the primary structure in the case considering the weight is smaller than that in the case ignoring the weight, but the difference decreases with the increase of the excitation amplitude. The experimental results demonstrate that considering the weight leads to more accurate predictions. [ABSTRACT FROM AUTHOR]

Abstract A parametric resonator for vibration energy harvesting is presented. Despite large responses from parametric resonance, two major drawbacks of parametric resonance harvesters are the high threshold excitation and narrow bandwidth. We addressed these two shortcomings by adding magnetic nonlinearity to the system. The proposed vibration energy harvester consists of two piezoelectric cantilevers beams, each with a magnetic tip. By controlling the distance between the two magnets, the threshold excitation level needed to trigger the parametric resonance decreases. Combining the softening and hardening behavior of the two magnetically coupled beams increases the frequency bandwidth. In addition, the amplitude of the response increases with the merger of the direct and parametric resonances of the two beams. We present a mathematical model of the system consisting of two lumped systems coupled by the magnetic force. The coupled governing equations are solved numerically, analytically, and are verified by experiments. Unique characteristics of wider bandwidth, larger response, and lower threshold excitation occur at the low frequency because of the added magnetic nonlinearity to the two-beam system. These properties can improve the efficiency of vibration energy harvesters. [ABSTRACT FROM AUTHOR]

Abstract Research on nonlinear isolation has always focused on the vibration of discrete systems. The elastic vibration of the main structure itself is always ignored. In order to study the influence of the multimodal elastic vibration of the main structure on the nonlinear isolation effect, nonlinear isolation of the transverse vibration of a pre-pressure elastic beam is studied in this paper. Three linear springs are utilized to build a nonlinear isolation system, in which horizontal springs are utilized to provide non-linearity and to achieve quasi-zero stiffness. The transverse vibration of the beam is isolated by the elastic support at the two ends. The Galerkin truncation method (GTM) is used to solve the response of the forced vibration. The isolation effect of the primary resonance of the pre-pressure beam is presented. The effects of the axial pre-pressure and nonlinear isolation system on vibration transmission are explored. Results of the GTM are confirmed by utilizing the finite difference method (FDM). It also illustrates the effectiveness of the proposed difference method for nonlinear support structures. The numerical results demonstrate that under certain conditions, the quasi-zero stiffness isolation system may increase the transmission of high-order modal vibration of the elastic continuum. Furthermore, this work finds that the initial axial pre-pressure could be beneficial to vibration isolation of elastic structures. [ABSTRACT FROM AUTHOR]

Abstract Predicting the response of gas turbine blades with underplatform friction dampers is challenging due to the combination of frictional nonlinearity and system uncertainty: a traditional Monte Carlo approach to predicting response distributions requires a large number of nonlinear simulations which is computationally expensive. This paper presents a new approach based on the principle of Maximum Entropy that provides an estimate of the response distribution that is approximately two orders of magnitude faster than Monte Carlo Harmonic Balance Method simulations. The premise is to include the concept of 'computational uncertainty': incorporating lack of knowledge of the solution as part of the uncertainty, on the basis that there are diminishing returns in computing precise solutions to an uncertain system. To achieve this, the method uses a describing function approximation of the friction-damped part of the system; chooses an ignorance prior probability density function for the complex value of the describing function based on Coulombs friction law; updates the distribution using an estimate of the mean solution, the admissible domain of solutions, and the principle of Maximum Entropy; then carries out a linear Monte Carlo simulation to estimate the response distribution. The approach is validated by comparison with HBM simulations and experimental tests, using an idealised academic system consisting of a periodic array of beams (with controllable uncertainty) coupled by single-point friction dampers. Comparisons with two- and eight-blade systems show generally good agreement. Predicting the response statistics of the maximum blade amplitude reveals specific well-understood circumstances when the method is less effective. Predictions of the overall blade response statistics agree with Monte Carlo HBM extremely well across a wide range of excitation amplitudes and uncertainty levels. Critically, experimental comparisons reveal the care that is needed in accurately characterising uncertainty in order to obtain agreement of response percentiles. The new method allowed fast iteration of uncertainty parameters and correlations to achieve good agreement, which would not have been possible using traditional methods. Highlights • A new approach to predict variability of friction-damped turbine blades is presented. • The method uses Maximum Entropy to estimate a PDF of the friction describing function. • Computationally expensive Monte Carlo simulations of the nonlinear system are avoided. • Comparisons with numerical and experimental tests show generally good agreement. • The method enables rapid estimates of the response distribution. [ABSTRACT FROM AUTHOR]

Abstract Friction dampers are often used to reduce high amplitude vibration within gas turbines: they are a robust solution that are able to withstand extreme operating environments. Although the turbine blades are manufactured to tight tolerances, there can be significant variability in the overall response of the assembly. Uncertainties associated with the frictional contact properties are a major factor contributing to this variability. This paper applies a recently developed method for predicting response bounds to friction-damped gas turbines when the characteristics of the friction dampers are unknown, including uncertainty regarding the underlying functional form of the friction law. The approach taken is to represent the frictional contact using a describing function, and formulate an optimisation problem to seek upper and lower bounds on a chosen response metric, such as displacement amplitude. Constraints are chosen that describe known properties of the frictional nonlinearity, without needing to specify a particular constitutive law. The method was validated by comparison with numerical and experimental results from an idealised test system. The experimental test rig consisted of an array of eight beams coupled by pin-contact friction dampers. A modal description of this test rig formed the basis of a numerical model, which uses the Harmonic Balance Method (HBM) for nonlinear simulations. A set of Monte Carlo tests was carried out numerically and experimentally for both a two-beam sub-assembly as well as for the full eight-beam assembly. Comparisons with numerical results showed excellent agreement providing confident verification of the implementation, and comparisons with experimental results revealed that the bounds became less conservative as the system complexity increased. Overall the results are promising: upper and lower response bounds for an array of friction-damped systems can be computed at similar cost to a single HBM simulation, giving reliable bounds that are valid for both parametric and model uncertainties associated with the friction couplings. Highlights • A new method to predict response bounds is applied to friction-damped systems. • The approach applies to parametric and model uncertainty associated with friction. • Bounds can be computed at similar computational cost to a single HBM simulation. • Results are compared with an eight-blade idealised laboratory test rig. • Comparisons with numerical and experimental Monte Carlo tests show good agreement. [ABSTRACT FROM AUTHOR]

Abstract This article explores the evolution of the nonlinear reduced-order modeling concept and its application to the acoustic fatigue problem as guided by a course of experiments. Since the advent of the jet engine, military aircraft have been plagued by acoustic fatigue. For decades, the resulting cracking has been a nuisance affecting mostly secondary structure, which can be routinely replaced. These thin aircraft panels are excited by ever increasing acoustic energy, causing the vibration to become nonlinear. The nonlinear response had been attributed to nonlinear damping but has been shown to be caused by geometric nonlinearity which results in nonlinear stiffness. Regardless of the cause of the nonlinearity, acoustic fatigue in conventional military aircraft can be controlled via damping treatments. However for high speed vehicles, the availability of high temperature damping treatments is practically non-existent. Furthermore, fatigue cracking in any part of the outer mold line can have catastrophic effects on the aerodynamic heating of these vehicles. Research into the prediction of the nonlinear vibration with reduced-order models has become popular in the past decade to address these concerns. This paper will document some experiences with these concepts through experimental investigations. [ABSTRACT FROM AUTHOR]

We present a theoretical and numerical investigation of the transverse dynamic response of monolithic Shape Memory Alloy (SMA) beams under the effect of axial pre-strains. The SMA beam is taken as benchmark structure to evaluate the effect of (axial) pre-strain on either the free or the forced dynamics. The combination of the static stress, produced by the pre-loading conditions, with the dynamic stress, associated with the vibratory response, affects the occurrence of the stress-induced SMA phase transformation hence providing a mechanism to passively tune the dynamic response. Particular attention is given to the effect that different pre-strain levels have on the overall ability to dissipate mechanical energy, that is on the effective damping. The numerical model of the SMA beam accounts for both material and geometric nonlinear behaviors. The nonlinear material behavior is due to the SMA phase-transformation and it is modeled via the one-dimensional improved Brinson's model (including tension–compression asymmetry), while the geometric nonlinear behavior is due to large displacements occurring during the phase transformation and it is accounted for via von Kármán assumptions. The resulting model is solved numerically via the finite element method and used to evaluate both the free and the forced response of the beam. The free response analysis suggests the existence of optimal pre-strain levels to achieve maximum damping capacity, while the forced response highlights the occurrence of nonlinear dynamic features, such as bifurcation. In both cases, it is found that the level of pre-strain can significantly affect the dynamic response as well as the effective damping. The results presented in this work provide useful guidelines to understand the dynamics of continuous SMA structures under pre-strain and the ability to tune either their resulting dynamics or dissipation properties. • Nonlinear dynamic analysis of monolithic SMA beams under varying operating conditions. • Effect of pre-strain on the damping capacity. • Improved stability illustrated via numerical bifurcation analyses. • Quantification of tunable damping capacity due to the SMA phase transition. [ABSTRACT FROM AUTHOR]

• A rotor-bearing system dynamics model of an axial piston pump is developed for analysing the misalignment–rubbing coupling fault. • According to the lumped-parameter model, the dynamic responses of the rotor-bearing system and the effects of model parameters are investigated. • A vibration experiment is performed on a rotor-bearing test rig to validate the rotor-bearing system dynamics model. Rotor-bearing system is widely utilised in axial piston pumps in which misalignment–rubbing mixed faults commonly occur, as rubbing and misalignment are both frequent and can occur simultaneously owing to the different working conditions. The dynamic behaviour of a rotor-bearing system misalignment–rubbing coupling defect supported by a ball bearing is complex. To examine the vibration characteristics of such faults, a rotor-bearing system model is established, and the dynamic responses of the rotor-bearing system with a misalignment–rubbing mixed fault are investigated under different parameters. The effects of the rotation speed, tilt misalignment, rubbing clearance, and rubbing stiffness on the rotor-bearing system with a misalignment–rubbing defect are examined via numerical simulations. Additionally, validation studies are conducted, and the results indicate that the distinctive frequency components may be useful for the detection of hybrid faults in rotor-bearing system. The degree of tilt misalignment has little influence on the rubbing frequencies. In the coupling fault, the rubbing fault is prominent. The frequency components of the system are dominated by high frequencies as the speed increases. The major fault feature in the frequency band is a double frequency. The numerical results are in agreement with the experiment. These results reveal the vibration characteristics of the rotor-bearing system for axial piston pump with misalignment-rubbing coupling fault. [ABSTRACT FROM AUTHOR]

This study analyzes the vibration reduction of a tuned mass damper (TMD) applied to a hinged-hinged nonlinear Euler-Bernoulli beam. We compare the effects of linear and nonlinear tuned mass dampers (LTMD/NLTMD) and obtain results undiscovered in previous studies. We analyze the frequency responses (fixed points) of the system using the method of multiple scales (MOMS) and obtain analytical solutions for the NLTMD in the frequency and time domains using Dimensional Analysis and the Perturbation Method. The present study shows that when the damping coefficient ( λ ), TMD mass ( m D ), TMD initial displacement ( A ) and nonlinear spring constant ( β ) of the NLTMD fulfill a function relationship λ = 3 m D β A , the damping and nonlinear elastic effects cancel each other out, and the nonlinear damping frequency coincides with the linear natural frequency. With a fixed damping coefficient and an LTMD or NLTMD at a fixed position, optimal damping is achieved when the product of the TMD mass and spring constant are at fixed values. Finally, we use the Floquet transition matrix of the system and Floquet multipliers (F.M.) to create the basin of attraction (BOA) and analyze the stability of the system under aerodynamic forces. [ABSTRACT FROM AUTHOR]

This discussion seeks to address some of the inconsistencies and concerns regarding fractional derivatives when applied to vibration analysis of viscoelastically damped beams [1]. Detailed numerical assessments of the major fractional derivatives of concern have been carried out with their relationships numerically examined. Numerical results have shown that two of the key equations of [1] are mathematically inappropriate and their applications could lead to serious modelling errors. A simplified yet representative nonlinear system with fractional viscoelastic damping and cubic stiffness nonlinearity is used to illustrate the existence of periodic steady-state solutions, as well as amplitude frequency characteristics of such fractional nonlinear systems. [ABSTRACT FROM AUTHOR]

The paper studies the transverse nonlinear vibration of an isotropic and homogeneous annular membrane spinning at constant angular velocity, under the action of a uniform transverse load. The equilibrium configuration of the membrane, clamped along the inner edge and free along the outer edge, and the natural frequencies of vibration of the membrane are calculated. A Galerkin procedure is used to determine a reduced order model describing the weakly nonlinear vibration of the membrane, and it is shown that near-resonance vibration can be modeled as a single degree of freedom Helmholtz-Duffing oscillator. A detailed study at vibration frequencies close to the fundamental, axisymmetric vibration mode shows a transition from softening to hardening behavior, and jump phenomena or hysteretic behavior depending on the angular velocity, the transverse load, the amplitude of dynamic excitation and the damping ratio. The results are in agreement with dynamic implicit finite element simulations in Abaqus/Standard and direct experimental measurements. [ABSTRACT FROM AUTHOR]

This paper presents a general formulation for nonlinear vibration analysis of rotating beams. A modified variational method combined with a multi-segment partitioning technique is employed to derive the free and transient vibration behaviors of the rotating beams. The strain energy and kinetic energy functional are formulated based on the order truncation principle of the fully geometrically nonlinear beam theory. The Coriolis effects as well as nonlinear effects due to the coupling of bending-stretching, bending-twist and twist-stretching are taken into account. The present method relaxes the need to explicitly meet the requirements of the boundary conditions for the admissible functions, and allows the use of any linearly independent, complete basis functions as admissible functions for rotating beams. Moreover, the method is readily used to deal with the nonlinear transient vibration problems for rotating beams subjected to dynamic loads. The accuracy, convergence and efficiency of the proposed method are examined by numerical examples. The influences of Coriolis and centrifugal forces on the vibration behaviors of the beams with various hub radiuses and slenderness ratios and rotating at different angular velocities are also investigated. [ABSTRACT FROM AUTHOR]

This study investigated the stability of vibration in a nonlinear suspension system with slow-varying sprung mass under dual-excitation. A mathematical model of the system was first established and then solved using the multi-scale method. Finally, the amplitude-frequency curve of vehicle vibration, the solution's stable region and time-domain curve in Hopf bifurcation were derived. The obtained results revealed that an increase in the lower excitation would reduce the system's stability while an increase in the upper excitation can make the system more stable. The slow-varying sprung mass will change the system's damping from negative to positive, leading to the appearance of limit cycle and Hopf bifurcation. As a result, the vehicle's vibration state is forced to change. The stability of this system is extremely fragile under the effect of dynamic Hopf bifurcation as well as static bifurcation. [ABSTRACT FROM AUTHOR]

Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account. [ABSTRACT FROM AUTHOR]

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately. [ABSTRACT FROM AUTHOR]

High-speed machinery is often designed to pass several “critical speeds”, where vibration levels can be very high. To reduce vibrations, rotors usually undergo a mass balancing process, where the machine is rotated at its full speed range, during which the dynamic response near critical speeds can be measured. High sensitivity, which is required for a successful balancing process, is achieved near the critical speeds, where a single deflection mode shape becomes dominant, and is excited by the projection of the imbalance on it. The requirement to rotate the machine at high speeds is an obstacle in many cases, where it is impossible to perform measurements at high speeds, due to harsh conditions such as high temperatures and inaccessibility (e.g., jet engines). This paper proposes a novel balancing method of flexible rotors, which does not require the machine to be rotated at high speeds. With this method, the rotor is spun at low speeds, while subjecting it to a set of externally controlled forces. The external forces comprise a set of tuned, response dependent, parametric excitations, and nonlinear stiffness terms. The parametric excitation can isolate any desired mode, while keeping the response directly linked to the imbalance. A software controlled nonlinear stiffness term limits the response, hence preventing the rotor to become unstable. These forces warrant sufficient sensitivity required to detect the projection of the imbalance on any desired mode without rotating the machine at high speeds. Analytical, numerical and experimental results are shown to validate and demonstrate the method. [ABSTRACT FROM AUTHOR]

Although there is considerable research on the experimental testing of foil-air bearing (FAB) rotor systems, only a small fraction has been correlated with simulations from a full nonlinear model that links the rotor, air film and foil domains, due to modelling complexity and computational burden. An approach for the simultaneous solution of the three domains as a coupled dynamical system, introduced by the first author and adopted by independent researchers, has recently demonstrated its capability to address this problem. This paper uses this approach, with further developments, in an experimental and theoretical study of a FAB-rotor test rig. The test rig is described in detail, including issues with its commissioning. The theoretical analysis uses a recently introduced modal-based bump foil model that accounts for interaction between the bumps and their inertia. The imposition of pressure constraints on the air film is found to delay the predicted onset of instability speed. The results lend experimental validation to a recent theoretically-based claim that the Gümbel condition may not be appropriate for a practical single-pad FAB. The satisfactory prediction of the salient features of the measured nonlinear behavior shows that the air film is indeed highly influential on the response, in contrast to an earlier finding. [ABSTRACT FROM AUTHOR]

Random excitation of mechanical systems occurs in a wide variety of structures and, in some applications, calculation of the power dissipated by such a system will be of interest. In this paper, using the Wiener series, a general methodology is developed for calculating the power dissipated by a general nonlinear multi-degree-of freedom oscillatory system excited by random Gaussian base motion of any spectrum. The Wiener series method is most commonly applied to systems with white noise inputs, but can be extended to encompass a general non-white input. From the extended series a simple expression for the power dissipated can be derived in terms of the first term, or kernel, of the series and the spectrum of the input. Calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived. The resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration. The results are validated both numerically and experimentally using a base-excited cantilever beam with a nonlinear restoring force produced by magnets. [ABSTRACT FROM AUTHOR]

• A multiscale computational paradigm is developed to study epoxy nonlinear vibration. • Mechanical properties enhance first and weaken subsequently under moisture effect. • Fundamental frequency of epoxy shows a similar variation as mechanical properties. • Epoxy has a lower level of nonlinear frequency ratio with 1.0 wt% moisture content. Epoxy thin films have been widely used in microelectromechanical systems, aerospace and civil engineering, which are exposed to external excitations in wet environment that lead to severe nonlinear vibration. In this paper, a multiscale simulation consisting of molecular simulation and meshless simulation is adopted to study moisture effect on nonlinear vibrations of epoxy thin film. In molecular simulations, the cross-linked epoxy molecules with moisture content from 0.0 to 4.0 wt% are constructed. It is measured that mechanical properties of epoxy molecules show an initial enhancement with moisture content from 0.0 to 1.0 wt%, and a subsequent decrease when moisture content increases to 4.0 wt%. With molecular simulation results as inputs, meshless simulations are carried out to investigate epoxy vibration behaviors, where vibration equations of epoxy thin films with investigated moisture contents are constructed and solved. It is determined that fundamental frequencies of epoxy thin films show a similar trend as the variation of mechanical properties. Meanwhile, the level of nonlinear frequency ratio decreases in 1.0 wt% case and subsequently increases up to 4.0 wt%. The vibration behaviors of epoxy thin film as revealed in this work contribute to the prediction of vibration behaviors of epoxy-based applications in wet environment. [Display omitted] [ABSTRACT FROM AUTHOR]

This study analyzes the obtained equations and results in “Varney and Green (2015) [1] ”. The analysis show that: (1) the state-space form of the differential equations in Eq. (16) is apparently incorrect; (2) since all results in the original article are extracted from the equations in state-space form, most of the results are consequently incorrect; (3) most of results shown as the graphs in the article are inconsistent with rotordynamics theory. The correct form of the equations and results are obtained, as well. As concluded in the present study, the equations and figures shown in Varney and Green (2015) [1] yield significantly incorrect behavior for the rotordynamics problem. [ABSTRACT FROM AUTHOR]

The problem of non-linear, steady state vibration of beams, harmonically excited by harmonic forces is investigated in the paper. The viscoelastic material of the beams is described using the Zener rheological model with fractional derivatives. The constitutive equation, which contains derivatives of both stress and strain, significantly complicates the solution to the problem. The von Karman theory is applied to take into account geometric nonlinearities. Amplitude equations are obtained using the finite element method together with the harmonic balance method, and solved using the continuation method. The tangent matrix of the amplitude equations is determined in an explicit form. The stability of the steady-state solution is also examined. A parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam's responses. [ABSTRACT FROM AUTHOR]

Recently-proposed techniques for the simultaneous solution of foil-air bearing (FAB) rotor dynamic problems have been limited to a simple bump foil model in which the individual bumps were modelled as independent spring-damper (ISD) subsystems. The present paper addresses this limitation by introducing a modal model of the bump foil structure into the simultaneous solution scheme. The dynamics of the corrugated bump foil structure are first studied using the finite element (FE) technique. This study is experimentally validated using a purpose-made corrugated foil structure. Based on the findings of this study, it is proposed that the dynamics of the full foil structure, including bump interaction and foil inertia, can be represented by a modal model comprising a limited number of modes. This full foil structure modal model (FFSMM) is then adapted into the rotordynamic FAB problem solution scheme, instead of the ISD model. Preliminary results using the FFSMM under static and unbalance excitation conditions are proven to be reliable by comparison against the corresponding ISD foil model results and by cross-correlating different methods for computing the deflection of the full foil structure. The rotor-bearing model is also validated against experimental and theoretical results in the literature. [ABSTRACT FROM AUTHOR]

Certain nonlinear vibrating systems have frequency response curves (FRCs), in which isolated detached curves exist inside the main continuous FRC. The behavior of these systems has hitherto been studied analytically and numerically, but to the authors’ knowledge, there is no record of an inner detached FRC being detected experimentally. These curves may be hidden by numerical or experimental analysis, particularly when a system is subject to swept or stepped-sine excitation. Their existence may thus lead to unexpected dramatic changes in the amplitude of the system response. This paper presents an experimental study that involves the design, construction and testing of a specific system that has an isolated detached FRC inside the main continuous FRC. The experimental design of the test rig is supported by multibody dynamic simulations, and in the experimental tests the existence of a detached FRC was verified. [ABSTRACT FROM AUTHOR]

This paper theoretically analyzes the nonlinear torsional vibration of a granular material specimen in the resonant column test (RCT). The RCT is a material testing method that has been well established in geotechnical engineering. The test provides some important dynamic properties of granular materials including the shear wave speed, effective dynamic shear modulus and damping capacity. Both the elastic modulus and damping capacity show a strong dependence on the amplitude of excitation, which is the essential behavior of materials with hysteretic nonlinearity. The analysis, starting with a constitutive relationship that describes the hysteretic nonlinear behavior of granular materials, is performed specifically on the forced torsional vibration of a circular bar with a fixed and inertia-loaded boundary condition as a model for the specimen in the RCT. Self-interaction of a single resonance mode is assumed in the perturbation analysis to obtain an approximate solution for near-resonance response. The theoretical results predict linear dependences of the resonance frequency and damping ratio on the shear strain; these are in agreement with the existing experimental observations. Notable is that the present model describes the hysteretic nonlinear behaviors with a single parameter, i.e., the hysteresis nonlinearity parameter in the constitutive relationship. The derived equations are applied to a jointed gneiss specimen where how the hysteresis nonlinearity parameter is determined from RCT data is demonstrated. [ABSTRACT FROM AUTHOR]

Active control is an attractive solution to the problem of structure-borne interior road noise in cars. However, nonlinear suspension dynamics could limit the cancellation that can be achieved with a linear feedforward road noise control system. The hydraulic dampers in a vehicle suspension have previously been found to be a source of nonlinear vibration transmission at low audio frequencies. This paper presents experimental measurements and modelling of the front and rear suspension dampers in a test vehicle aimed at understanding the physical processes causing their nonlinear dynamics. Experiments are shown that highlight the different nonlinear effects present in the dampers, including friction and the mechanics of the piston valves. A suitable model was then selected from the literature, fitted to the measurements and validated. Analysis of the models revealed that, in the front damper, both friction and the valve mechanics contribute significantly to the damper's nonlinear dynamics between 50–300 Hz. Friction in the rear damper is much less significant, meaning that its nonlinear dynamics are almost entirely caused by the piston valves. Although the front damper's friction behaviour proved challenging to model, the effect of the piston valves was captured very accurately in both damper models. • Experiments and modelling identify important nonlinear processes in two suspension dampers. • Nonlinear vibration transmission in the front damper is due to friction and the valves. • Friction in the rear suspension damper is less significant than in the front. • Nonlinear vibration transmission in the rear damper almost entirely due to the valves. [ABSTRACT FROM AUTHOR]

• A geometric nonlinear energy harvester with quad-stability is considered. • The amplitude frequency response is obtained by the complex dynamic frequency method. • The primary resonance and subharmonic resonance are detailed discussed. • Multiple vibration patterns have been determined experimentally. • Experiment verifies the effectiveness of the dynamic theoretical method. In this paper, a quad-stable piezoelectric vibration energy harvester induced by the geometric nonlinearity of springs is designed and investigated. The novelty is that by replacing the permanent magnets with a combination of springs, the system can be effectively protected from electromagnetic interference in the working environment. The innovative design of three hinged springs attached to the tip of the cantilever beam makes the stiffness of the structure inherently nonlinear, which can induce the multi-stability of the system. The Euler-Lagrange equations are applied to establish the governing equation of the energy harvester. The static bifurcation analysis reveals the evolution process of multi-stability. The complex dynamic frequency (CDF) method, an efficient approach to solving strongly nonlinear dynamic problems with multi-well systems, is then applied to deduce the system's amplitude-frequency response. Combinations of theoretical and numerical results show that among a wide frequency bandwidth, the system can exhibit such as single-, double- and quadruple-well periodic motions. Finally, experiments are set up to verify the advantage of inter-well motion on harvesting power. Result shows that geometric nonlinearity can effectively make the energy harvester exhibit multi-stability, generate different movement patterns, and obtain high harvesting power. [ABSTRACT FROM AUTHOR]

• Simulated a 3-D model of an aerospace spiral bevel gear pair by face milling approach. • Verified the FEM results with the experimental data by extracting maximum principal stress on the root of the tooth. • Calculating the mesh stiffness with a suitable accuracy based on loaded and unloaded tooth contact analyses. • Solved the nonlinear governing equation by the numerical integration based on an adaptive step-size implicit Runge-Kutta scheme. • Considered the probability of backside contact by calculating and considering the real mesh stiffness for reverse direction. • Investigation the influences of backlash and damper ratio on the nonlinear dynamic behavior of face-milled spiral bevel gear. In the present paper non-linear dynamics of a spiral bevel gear pair with backlash are investigated in order to clarify the internal excitations of major importance from the vibration point of view: manufacturing errors in the teeth profile, teeth spacing errors, and elastic deformation of the teeth. In some conditions, like in the case of backside contact, the destructive effect of internal excitations can be intensified leading to complex dynamics; for such reasons here backside contacts and reverse rotation are investigated in detail using a nonlinear time-varying model. The effect of damping is investigated as well. A one-DOF model is developed in order to study the dynamic behavior; the resulting a nonlinear differential equation with time-varying mesh stiffness is solved via numerical integration based on an adaptive step-size implicit Runge-Kutta scheme. The dynamic response of the system is analyzed through time histories, phase portraits, bifurcation diagrams, and Poincaré maps. Results show that for small backlash values, the possibility of backside contact increases. Meanwhile, by increasing the backlash value, the amplitude vibration of the gear rotation rises as well. By comparing the dynamic response of the system with different damping ratios, the results show that higher damping effectively reduces gear vibration resonance, although the probability of unsteady response still exists. [ABSTRACT FROM AUTHOR]

The nonlinear vibration response of an assembly with friction joints – named “Harmony” – is studied both experimentally and numerically. The experimental results exhibit a softening effect and an increase of dissipation with excitation level. Modal interactions due to friction are also evidenced. The numerical methodology proposed groups together well-known structural dynamic methods, including finite elements, substructuring, Harmonic Balance and continuation methods. On the one hand, the application of this methodology proves its capacity to treat a complex system where several friction movements occur at the same time. On the other hand, the main contribution of this paper is the experimental and numerical study of evidence of modal interactions due to friction. The simulation methodology succeeds in reproducing complex form of dynamic behavior such as these modal interactions. [ABSTRACT FROM AUTHOR]

Nonlinear energy harvesters are very sensitive to ambient vibrations. If the excitation level is too low, their large-amplitude oscillations for high-energy voltage output cannot be obtained. A nonlinear tristable energy harvester has been previously proposed to achieve more effective broadband energy harvesting for low-level excitations. However, the sensitivity of its dynamic characteristics to the system parameters remains uninvestigated. Therefore, this paper theoretically analyzes the influence of the external load, the external excitation, the internal system parameters and the equilibrium positions on the dynamic responses of nonlinear tristable energy harvesters by using the harmonic balance method. In addition, numerical acceleration excitation thresholds and basins of attraction are provided to investigate the potential for energy harvesting performance enhancement using the suitable equilibrium positions, appropriate initial conditions or external disturbances, due to high-energy interwell oscillations in the multi-solution ranges. More importantly, experimental voltage responses of a given tristable energy harvester versus the external excitation frequency and amplitude verify the existence of experimental multi-solution ranges and the effectiveness of the theoretical analysis. It is also revealed that achieving high-energy interwell oscillations in the multi-solution ranges of tristable energy harvesters will be feasible for improving energy harvesting from low-level ambient excitations. [ABSTRACT FROM AUTHOR]

Detached resonance curves have been predicted in multi-degree-of-freedom nonlinear oscillators, when subject to harmonic excitation. They appear as isolated loops of solutions in the main continuous frequency response curve and their detection may thus be hidden by numerical or experimental analysis. In this paper, an analytical approach is adopted to predict their appearance. Expressions for the amplitude-frequency equations and bifurcation curves are derived for a two degree-of-freedom system with cubic stiffness nonlinearity, and the effect of the system parameters is investigated. The interest is specifically towards the occurrence of closed detached curves appearing inside the main continuous frequency response curve, which may lead to a dramatic reduction of the amplitude of the system response. Both cases of hardening and softening stiffness characteristics are considered. The analytical findings are validated by numerical analysis. [ABSTRACT FROM AUTHOR]

• A new geometrically exact model of fluid-conveying curved pipes is established. • Dynamical behavior of the curved pipe can be well predicted by the GE model. • The curved pipe may undergo large-amplitude deformation due to fluid excitation. • The curved pipe vibrates periodically with sufficiently high flow velocity. Fluid-conveying flexible pipes are widely used in the fields of soft robots and biological medicine. In recent years, considerable progress has been made in investigating the dynamics of initially straight pipes. However, due to the lack of effective theoretical models for flexible pipes undergoing large deformation, the mechanism governing the dynamics of curved pipes conveying fluid is still unclear. In this work, a geometrically exact (GE) model of fluid-conveying flexible pipes with arbitrary initial configuration is established. The validation of this new theoretical model and the employed numerical algorithm is conducted by comparing the current results with that based on the absolute nodal coordinate formulation (ANCF). Based on this GE model, the static deformation, stability and nonlinear vibration of a semi-circular pipe are systematically studied. It is shown that the large-deformation behaviors of the flexible curved pipe can be well predicted by the newly developed GE model. In addition, the effects of mass ratio, flow velocity and gravity parameter are discussed, and some conclusions are drawn. The proposed theoretical model and simulation results for large deformation of fluid-conveying curved pipes are also expected to be useful in the prediction, design and control of the dynamical behavior of various initially curved pipes in practical engineering. [ABSTRACT FROM AUTHOR]