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Analysis of vibration stability of simply supported Euler-Bernoulli functionally graded (FG) nanobeam embedded in viscous elastic medium with thermal effect under external parametric excitation is presented in this work. An attempt has been made for the first time is investigating the effect of thermal load on dynamic behavior, amplitude response, instability region and bifurcation points of functionally graded nanobeam. Thermal loads are supposed to be uniform, linear or nonlinear distribution along the thickness direction. Nonlocal continuum theory and the principle of the minimum total potential energy are applied to derive the governing equations. The partial differential equations (PDE) are transported to the ordinary differential equations (ODE) by using the Petrov-Galerkin method and the multiple time scales method are manipulated to solve the motion equation. To study the effect of external parametric excitation and thermal effect, different temperature distributions along the thickness such as uniform, linear, and nonlinear distribution are considered. Moreover, stable and unstable regions and bifurcation points are determined. It is obtained that the thermal load can affect the amplitude response of FG nanobeam. Also, it is observed that the instability of the system is affected by the detuning parameter and the parametric excitation amplitude plays great role in the instability of system. Nanobeams are used in many devices like nanoresonators, nanosensors and nanoswitches. This paper is helpful for designing and manufacturing nanoscale structures specially nanoresonators under different thermal loads.

The lattice sandwich structure is a new type of artificial structure developed in recent years. It is light in weight and rigid in stiffness, which is naturally suitable for the aviation engineerin...

In order to control the vibration of the involute spline coupling in aeroengine well and reduce the fretting wear, a bending–torsion coupling nonlinear vibration model of the involute spline coupling with the misalignment was proposed, and a dynamic meshing stiffness function with multiteeth engagement was established. Then, the influence of different misalignment, wear, and rotation speeds with different misalignment on the nonlinear vibration characteristics of the involute aviation spline coupling was explored. The result shows that with an increase of the parallel misalignment, the system experienced the state of a single period, a quasiperiod, multiperiod, and chaos but finally only alternated between the quasiperiod and the chaos state. The uneven wear of each tooth of the spline displayed a significant influence on the vibration of the spline coupling, and the influence of the uniform wear was smaller under given conditions here. Furthermore, with an increase of the speed, the larger the misalignment was, the more times the system entered or left the chaos state were. The model proposed here is found to be closer to the actual working conditions, and the analysis results can provide more accurate external load conditions for the prediction of the fretting damage of the spline coupling in aeroengine.

In gear transmissions, vibration causes noise and malfunction. In actual applications, misalignments contribute to intensifying the destructive effect of vibrations. In this paper, the nonlinear dynamics of a spiral bevel gear pair, with small helix angle, considering different misalignments, are deeply investigated. Axial misalignment, radial misalignment, and the combination of these two types are considered in this study. The governing equation is numerically solved through an implicit Runge–Kutta scheme. Since the main goal of this study is the analysis of the dynamic scenario, the mesh stiffness of the gear pair is obtained from the literature. The dynamical system is nonlinear and time-varying, it is analyzed through time responses, phase portraits, Poincaré maps, and bifurcation diagrams. Results show that, among the considered three cases with different types of misalignments, the spiral bevel gear with axial misalignment is the worst destructive case, aperiodic, subharmonic, and multiperiod responses are observable for this case. It is interesting that the chaotic responses for the case, having both types of misalignments, are less likely for the case with axial misalignment, only.

Nonlinear phenomena widely occur in practical engineering applications. A typical example in aerospace structures is the creation of a breathing crack that opens and closes under cyclic loads, which causes bilinear behavior in the structural response. Late detection of such cracks can lead to a catastrophic failure that results in extensive structural damage. Therefore, analyzing the behavior of the structure because of the presence of a breathing crack is very important and needs to be investigated in detail. In this article, the nonlinear response of a single-degree-of-freedom nonlinear cantilever beam with a transverse breathing crack and bilinear behavior was studied. To investigate the nonlinear behavior, bilinear functions of the beam stiffness and nonlinear geometric stiffness were converted to polynomial functions. The proposed model is validated by comparing the time history responses of the approximated polynomials with the bilinear model of the cracked beam. Moreover, by considering damping changes because of the presence of the breathing crack, the nonlinear behavior was investigated. The results indicated that the proposed method is sensitive to the presence of a breathing crack. Also, the nonlinearity increases with an increase in the crack depth and location ratios associated with the jump phenomenon in the vibration response of the cracked beam.

Different numerical schemes are introduced to formulate and solve nonlinear vibration analysis of elastically supported multilayer composite plate problems. The type of elastic foundation is Winkle...

In this paper, the nonlinear vibration of railway track systems resting on elastic foundation has been studied. An axially loaded simply supported Euler–Bernoulli beam resting on a flexible foundation has been considered to provide a mathematical representation of the railway track system. Winkler springs have been used to model the elastic foundation. Nonlinear partial differential equation of the system has been presented and solved. A new approximate analytical solution called Improved Amplitude–Frequency Formulation (IAFF) is proposed to obtain nonlinear frequency of the system and an accurate analytical solution for the whole domain. The first iteration of the IAFF leads to a highly accurate solution in comparison with the exact frequency of the problem. The exact frequency of the problem is also presented, and the results of IAFF are compared and verified. Sensitive analysis of the soil stiffness and loading condition is studied for different parameters. A full comparison of the IAFF and exact solution results are illustrated. It has been proved that the IAFF can be potentially extended to highly nonlinear conservative problems.

This paper has investigated the semi-analytical analysis of the solid-fluid interaction vibration in the presence of concentrated mass-spring-damper vibration absorber. The nonlinear partial differential equations of motion are derived by considering von Karman-type large deformations and viscoelastic behaviour. Fluid-structure interaction is modelled by using an acceleration coupling model in which a nonlinear Van der Pol oscillator simulates fluctuating nature of the vortex street. The nonlinear equations are discretized via the Galerkin approach, and the obtained equations are numerically solved by applying the Runge-Kutta method. Eventually, the dynamic response, phase plane plots, and variations of maximum amplitude in terms of fluid velocity for different parameters are extracted. The results reveal that utilizing vibration absorber leads to a significant effect on the dynamic characteristics of the system, displaces the lock-in phenomenon, and remarkably reduce the amplitude of the system oscillations.

Long service time and excessive vibration of aero-engine will cause failure of clamps, which usually fix pipelines on the outside of an aero-engine. In this paper, the nonlinear vibration characteristics caused by loosening clamps in aero-engine pipeline are determined. According to the real parameters of an aero-engine clamp-pipeline test rig, the clamp is simplified into a nonlinear spring-damping. Thus, a clamp-pipeline nonlinear model based on cubic stiffness is established. The multi-scale method is used to obtain the analytical solution of the nonlinear model. Based on the real test data, the model parameters of the clamp-pipeline nonlinear system are identified, and then the nonlinear vibration characteristics of the system are obtained. Finally, using the vibration transmissibility method, the influence of the severity of clamp loosening on the nonlinear vibration characteristics of the system is obtained.

There exists a lot of research on the nonlinear vibration of the pipeline system with different boundary conditions. To the best of our knowledge, little research on the actual constraint of the clamp has been performed. In this paper, according to hysteresis loops of the clamp obtained from experimental test, the simplified bilinear stiffness and damping model is proposed. Then the Finite Element (FE) model of L-type pipeline system with clamps is established using Timoshenko beam theory in combination with aforementioned stiffness-damping model. Both hammering and shaker tests verify the FE model via the comparisons of natural frequencies and vibration responses. The results show that the maximum errors of natural frequencies and vibration responses are about 8.31% and 17.6%, respectively. The proposed model can simulate the dynamic characteristics of the L-type pipeline system with clamps well, which is helpful to provide some guidance for the early design stage of pipeline in aero-engine.

This paper is devoted to investigate the nonlinear vibration characteristics and active control of composite lattice sandwich plates using piezoelectric actuator and sensor. Three types of the sandwich plates with pyramidal, tetrahedral and Kagome cores are considered. In the structural modeling, the von Karman large deflection theory is applied to establish the strain–displacement relations. The nonlinear equations of motion of the structures are derived by Hamilton’s principle with the assumed mode method. The nonlinear free and forced vibration responses of the lattice sandwich plates are calculated. The velocity feedback control (VFC) and H∞ control methods are applied to design the controller. The nonlinear vibration responses of the sandwich plates with pyramidal, tetrahedral and Kagome cores are compared. The influences of the ply angle of the laminated face sheets, the thicknesses of the lattice core and face sheets and the excitation amplitude on the nonlinear vibration behaviors of the sandwich plates are investigated. The correctness of the H∞ control algorithm is verified by comparing with the experiment results reported in the literature. The controlled nonlinear vibration response of the sandwich plate is computed and compared with that of the uncontrolled structural system. Numerical results indicate that the VFC and H∞ control methods can effectively suppress the large amplitude vibration of the composite lattice sandwich plates.

Reinforced concrete structures experience nonlinear vibration response because of softening in concrete due to damage, which results in unstable vibration. Thus, considering the nonlinearity in vibration for assessment of damage is imperative to identify the actual damage scenario. Nonlinearity is predominant during the initial stage of damage when cracks start developing in the concrete exhibiting nonlinear breathing-crack mechanism. By suitably extracting nonlinear features from ambient/forced vibration, information on initial stage of damage (primarily breathing-crack) in large concrete structures can be obtained. In the present study, evaluation of nonlinear dynamic features from an experimental model of a reinforced concrete bridge girder-deck system is investigated. The damage scenarios in the bridge girder is experimentally simulated by monotonically applied static load at different levels. Vibration responses are acquired using the accelerometers positioned at regular intervals, so that the global system behaviour can be assessed. Damage features at various damage levels are evaluated based on the signal statistics, amplitude dependency, harmonics, phase-plane information and so on. The breathing-crack behaviour of the bridge girder during initial damage stages is investigated and the existence of sub- and super-harmonic components in the frequency spectra is distinctly evidenced and their amplitudes are quantified. The change of skewness pattern of the frequency spectra with increasing damage level is also evaluated. A distinct variation in phase space portrait is observed with increase in damage levels. It is found that, in spite of presence of inherent material nonlinearity, nonlinearity caused through system damage, even at initial stages of damage, is predominant and could be distinctly captured without any baseline information. The identified nonlinear vibration characteristics showed a remarkable relevance in detecting breathing-crack type damage in weakly nonlinear bridge. The investigated damage features from this study would pave the way for real-time baseline free assessment and identification of damage in concrete structures.

Vibration mitigation is essential to many dynamical and engineering structures that are subjected to destructive vibration amplitudes induced by impulsive loading, seismic excitation, blasts, flutter, collisions, fluid–structure interaction and so on. Unprotected structures by vibration absorbers could be exposed to failure which lead to enormous losses in human lives, major equipment and economy. Employing the nonlinear targeted energy transfer (TET) concept in nonlinear vibration absorbers which are later called as nonlinear energy sinks has ignited a very rapid research interest since 2001. Up-to-date, considerable growth in the NESs field has taken place. Accordingly, various types of NESs have been introduced for vibration mitigation in variety of dynamical and structural engineering systems. The types of introduced NESs included, but not limited to, stiffness-based, rotating and the vibro-impact NESs. Among these common types of NESs, the most effective and efficient one is the single-sided vibro-impact (SSVI) nonlinear energy sink (NES). However, most of investigations has implemented a coefficient of restitution of 0.7 which closely corresponds to a steel-to-steel impact. Therefore, this paper is aimed to further improve the SSVI NES by including the coefficient of restitution in the performance optimization. Accordingly, significant improvement in the SSVI NES performance is obtained when the coefficient of restitution is found to be near 0.45. In addition, performance comparison between the enhanced SSVIe NES with several existing types of NESs is performed here where a nine-story large-scale structure is employed for this numerical comparison. Accordingly, the performance of the enhanced SSVIe NES of nearly 0.45 coefficient of restitution is found to be more robust to the initial impulsive energy levels and to its physical parameters variation than other kinds of existing NESs.

This work attempts to study the vibration response of a double-row self-aligning ball bearing due to surface and localized imperfections. For the contact deformation at the ball–race interactions, the Hertzian load–deflection relation is used for the evaluation of time-varying contact stiffness. The elastohydrodynamic theory is applied to find out the central film thickness. For both the inner and outer race waviness cases, the system response is observed as periodic (with vibrations of high amplitude) at [Formula: see text], i.e. multiples of Nb and its vicinity, but gradually turns to quasi-periodic as the value of waviness order reach some intermediate value. In the case of a localized defect, the double impulse phenomenon marks the entry and exit events of the rolling element in and out of the rectangular spall. Hence, this analysis can be used as a diagnostic tool with system dynamic characteristics for distributed and localized defect identification.

A typical quasi-zero stiffness (QZS) vibration isolator composed of two lateral springs and a vertical spring has been widely studied previously, aiming to widen the frequency range of isolation without increasing the static displacement. However, there is still a gap between the previous dynamic model and the practical application, due to the neglection of some factors that may exist in practical situations. In this paper, a more accurate dynamic model is established with consideration of these practical factors. The dynamic behavior and dynamic characteristics of this typical QZS isolator are analyzed based upon the accurate dynamic model. The biggest difference between the newly proposed dynamic model and the previous one lies in the damping characteristics. Therefore, we specially investigate the damping effects, from which it is found that the vibration isolation performance can be further enhanced by proper design of the damping parameters.

Nonlinear vibration of rotating machinery induced by rolling bearings has gradually become a research issue. In many cases, the rotor discs are not always installed in middle of shaft in actual rotor system, and the influence of disc offset on nonlinear vibration needs to be studied in depth as rotating speed increases. This study deals with the effect mechanism of rotor offset on nonlinear dynamic responses. Nonlinear vibration model of offset rotor is established based on finite element method, and the disc offset position along rotor shaft is concerned. The responses are calculated by Newmark-β integration method, which are also validated by an experimental rig, and the influences of nonlinear parameters of rolling bearings are investigated. The results indicate that disc offset is a crucial factor that can induce more complex nonlinearity coupled with rolling bearing under high-speed conditions.

This study is aimed at investigating the effects of intermediate support stiffness on nonlinear vibration response of transmission system. A coupled bending–torsional–lateral dynamic model with 14 degrees of freedom of transmission system is proposed comprehensively considering rubber dynamic stiffness, time-varying stiffness, static transmission error, and backlash. Meanwhile, a model of intermediate support with rubber nonlinear properties is developed to improve the accuracy of analysis. On the basis of the nonlinear differential equations derived by the lumped-parameter method, the dynamic responses of the key parts in the transmission system are obtained using the Runge–Kutta method and the effects of intermediate support stiffness on the dynamic characteristics are analyzed. Numerical results show that complicated interaction occurs and intermediate support stiffness has a great influence on the vibration of the coupled system. With the increase in the intermediate support stiffness, the vibration displacements in the three directions of the gear are progressively reduced and the nature frequencies are changed. The influence of the radial stiffness is greater than that of the axial stiffness. An experiment is performed subsequently to validate the effect of intermediate support stiffness on system, and the experimental results are consistent with numerical ones.

The numerical analysis for cable nonlinear vibration with external viscous damper based on explicit integration equation of motion is proposed. The algorithm allows taking into account both the geometry non-linearity of the cable and the non-linearity associated with the damper. There has been made an analysis of free nonlinear vibration to determine the total vibration decrement of the system with damper. The optimal parameters for external viscous damper are determined. There have been obtained dependences for damping system optimal parameters in relation to the reduced damper coordinate.

This paper provides a review of models and solutions for the buckling and postbuckling of beams available from the 50s of the last century to date. Beams with axially unrestrained (movable) ends and restrained (immovable) ends are covered. In each class, the formulation of the nonlinear buckling problem for the buckling loads and the postbuckling states is discussed and the underlying assumptions are highlighted. For relatively large-amplitude buckling of beams with movable ends, approximate analytical solutions up to the third order are presented and compared with the exact solutions expressed in terms of elliptic integrals. For beams with immovable ends, buckling involves midplane stretching that makes the nonlinear buckling problem takes the same form of the standard eigenvalue problem and, hence, exact solutions are affordable. This review combines the research outcomes on buckled beams from two scientific viewpoints: the structural dynamics and the nonlinear vibration viewpoints, respectively. Moreover, it presents in one place the formulation and the exact solutions for the buckling of beams to serve as an on-demand resource for researchers concerned with the buckling and postbuckling of beams.

Linear and nonlinear normal mode motions may provide promising information about the condition of mechanical structures under small and large amplitude vibrations, respectively. In this view, this study investigates the nonlinear dynamics of cracked beams through use of the nonlinear mode motion and extends the crack identification methods that utilize the linear characteristics to nonlinear vibrating structures. At first, the nonlinear normal modes of the intact and cracked beams are calculated by a continuation algorithm. A finite element model of a geometrically nonlinear prismatic beam was created based on crack stress intensity. Subsequently, a method based on normal mode motion and minimization of strain energy, which is valid for linear and nonlinear vibrating beams, was developed as an optimization problem. To this end, hybrid optimization was also used due to its capability in finding global minimum along with its computational efficiency. It was shown that the proposed crack detection technique is applicable to beams vibrating in linear and/or nonlinear regimes and well capable of detecting both crack location and severity.

Rotating blade is one of the most important components for turbomachinery. Blade crack is one of the most common and dangerous failure modes for rotating blade. Therefore, the fault mechanism and feature extraction of blade crack are vital for the safety assurance of turbomachinery. This study is aimed at the nonlinear dynamic model of rotating blade with transverse crack and the prior feature extraction of blade crack faults based on the vibration responses. First and foremost, a high-fidelity breathing crack model (HFBCM) for rotating blade is proposed on the basis of criterion for stress states at crack section. Since HFBCM is physically deduced from the perspective of energy dissipation and the coupling between centrifugal stress and bending stress is considered, the physical interpretability and the accuracy of the crack model are enhanced comparing with conventional models. The validity of the proposed HFBCM is verified through the comparison study among HFBCM, conventional crack models, and finite element-based contact crack model (FECCM). It is suggested that HFBCM behaves best among the analytical models and matches well with FECCM. With the proposed HFBCM, the nonlinear vibration responses are investigated, and four types of blade crack detection indicators for rotating blade and their quantification method are presented. The numerical study manifests that all these indicators can well characterize the occurrence and severity of crack faults for rotating blade. It is indicated that these indicators can serve as the crack-monitoring indexes.

In this paper, the nonlinear vibration characteristics and optimization analysis of the diaphragm pump valves are studied. Considering the coupling effect between the fluid and structures, the dynamic equations of the quality valve for the diaphragm pump is established by analyzing the force equilibrium of the quality valves. The spring preload can be obtained through analyze fluid flow between the alve lift and the structural parameters. The key parameters of quality valve for the diaphragm pump are obtained by the experimental testing data. The dynamic equation of quality valve is solved by using the fourth-order Runge-Kutta method. The nonlinear vibration characteristics of the quality valve are analyzed, and the influences of the valve clearance circumference and other structure parameters on the nonlinear vibration characteristics are also discussed. Moreover, the optimization analysis of the structural parameters for the quality valve for the diaphragm pump is conducted in order to reduce the vibration of the quality valves. The analysis model and method proposed in this article provide a new design process for quality valves of the diaphragm pump.

This research proposes an energy harvesting system that collects the downward airflow from a helicopter or a multi-axis unmanned rotary-wing aircraft and uses this wind force to drive the magnet to rotate, generating repulsive force, which causes the double elastic steel system to slap each other and vibrate periodically in order to generate more electricity than the traditional energy harvesting system. The design concept of the vibration mechanism in this study is to allow the elastic steel carrying the magnet to slap another elastic steel carrying the piezoelectric patch to form a set of double elastic steel vibration energy harvesting (DES VEH) systems. The theoretical DES VEH mechanism of this research is composed of a pair of cantilever beams, with magnets attached to the free end of one beam, and PZT attached to the other beam. This study analyzes the single beam system first. The MOMS method is applied to analyze the frequency response of this nonlinear system theoretically, then combines the piezoelectric patch and the magneto-electric coupling device with this nonlinear elastic beam to analyze the benefits of the system’s converted electrical energy. In the theoretical study of the DES VEH system, the slapping force between the two elastic beams was considered as a concentrated load on each of the beams. Furthermore, both SES and DES VEH systems are studied and correlated. Finally, the experimental data and theoretical results are compared to verify the feasibility and correctness of the theory. It is proven that this DES VEH system can not only obtain the electric energy from the traditional SES VEH system but also obtain the extra electric energy of the steel vibration subjected to the slapping force, which generates optimal power to the greatest extent.

In deep-water test conditions, the riser-test pipe system (RTS) is subject to the vortex induced effect on riser, flow induced effect on test pipe and longitudinal/transverse coupling effect, which is prone to buckling deformation, fatigue fracture and friction perforation. To resolve this, the three-dimensional (3D) nonlinear vibration model of deep-water RTS is established using the micro-finite method, energy method and Hamilton variational principle. Based on the elastic-plastic contact collision theory, the nonlinear contact load calculation method between riser and test pipe is proposed. Compared with experimental measurement results, calculation results of the proposed vibration model in this study and the single tubing vibration model in our recent work, the correctness and effectiveness of the proposed vibration model of the deep-water RTS are verified. Meanwhile, the cumulative damage theory is used to establish the fatigue life prediction method of test pipe. Based on that, the influences of outflow velocity, internal flow velocity, significant wave height, as well as top tension coefficient on the fatigue life of test pipe are systematically analyzed. The results demonstrate that, first, with the increase of outflow velocity, the maximum alternating stress, the annual fatigue damage rate increased and the service life decreased significantly. The locations where fatigue failure of the test tube is easy to occur are mainly distributed at the upper “one third” and the bottom of test pipe. Second, with the increase of internal flow velocity, the “one third effect” of the test pipe will decrease, and is shown “the bottom damage effect”, which needs the attention of field operators. Third, during field operation, it is necessary to properly configure the top tension coefficient so that there can be a certain relaxation between the riser and the test pipe, so as to cause transverse vibration and consume some axial energy and load. The study led to the formulation of a theoretical method for safety evaluation and a practical approach for effectively improving the fatigue life of deep-water test pipe.

A semi-analytical approach of nonlinear vibration of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) plates and cylindrical panels stiffened by longitudinal or transversal FG-CNTRC stiffeners by using the first-order shear deformation theory (FSDT) with the geometrical nonlinearities in von Karman sense is reported in this paper. The novel smeared stiffener technique is improved for FG-CNTRC stiffeners according to the FSDT. The stress function is considered and the Galerkin method is used to formulate the nonlinear motion equation system, and dynamic responses of panels are obtained by using the fourth order Runge-Kutta method. Numerical investigations can show the very large effects of FG-CNTRC stiffeners, volume fraction of carbon nanotube, type of carbon nanotube distribution of panels and stiffeners with different geometrical parameters on the nonlinear vibration behaviors of stiffened FG-CNTRC plates and cylindrical panels.

Before the final experimental validation and certification of a turbo-engine, designers perform a numerical simulation of its vibratory properties, among other things, in order to estimate its lifespan and adjust the design in an optimization process. One possible practical solution to decrease the vibratory response is to add underplatform dampers to the system. These components dissipate energy by friction and are widely employed in turbomachinery. However, a specific underplatform damper is usually efficient only for a specific mode. The purpose of this work is to investigate the possibility of adding different kinds of underplatform dampers to the cyclic structure in order to decrease the vibratory energy over a larger panel of modes. Different methods exist to determine the vibrations of nonlinear cyclic symmetric systems, but creating a robust methodology to account for the additional effect of mistuning remains a big challenge in the community. In this paper, the structure is mistuned through the friction coefficient of the dampers and not by altering its geometry, as is usually done in the literature. First, assuming a cyclic symmetric structure, the performance of the dampers is assessed for specific modes. Then, employing a method recently developed, the efficiency of an intentional mistuning pattern of underplatform dampers is studied and an optimal pattern proposed.

As sophisticated mechanical equipment, the rotor system of aero-engine is assembled by various parts; bolted flange joints are one of the essential ways of joints. Aiming at the analysis of the nonlinear vibration characteristics of the rotor-bearing system with bolted flange joints, in this paper, a finite element modeling method for a rotor-bearing system with bolted flange joints is proposed, and an incremental harmonic balance method combined with arc length continuation is proposed to solve the dynamic solution of the rotor system. In order to solve the rotor system with rolling bearing nonlinearity, the alternating frequency/time-domain process of the rolling bearing element is deduced. Compared with the conventional harmonic balance method and the time-domain method, this method has the characteristics of fast convergence and high computational efficiency; solving the rotor system with nonlinear bearing force; overcome the shortcoming that the frequency–response curve of the system is too sharp to continue solving. By using this method, the influence of bearing clearance and stiffness on vibration characteristics of the rotor system with bolted flange joints is studied. The evolution law of the state of the rotor system with bolt flange is investigated through numerical simulation and experimental data. The results indicated that the modeling and solving method proposed in this paper could accurately solve the rotor-bearing system with bolted flange joints and analyze its vibration characteristics.

A brief overview of the achievements of the Mekhanobr Institute in the field of the theory and design of vibration processes and machines is given. The main theoretical works cover the discovery and development of the theory of self-synchronization of rotating bodies, the development of the theory of vibrational displacement, the creation of new analytical approaches to studying the effects of vibration on nonlinear systems and media – vibrational mechanics and vibrational rheology; the discovery and research into a number of nonlinear vibration effects, the development of the theory of vibrational classification. The main applied developments include the creation of a new class of highly efficient vibration machines (crushers, screens, separators, flotation machines, etc.), the development of respective design methods, the creation of a set of laboratory vibration equipment and a unique experimental base. The developments of recent years are considered in detail.

This paper focuses on the steady vibration characteristics of the bladed-disk subjected to the dry friction damping under periodic excitation. The multi-harmonic method and continuation procedure are combined to trace the solution of the nonlinear forced vibration problem. To obtain a stable and fast nonlinear solver, the analytical formulation of Jacobian matrix in frequency-domain is derived for elastic Coulomb friction model with variable normal force. Furthermore, the continuation method is generalized to trace the solution via different parameters, including not only commonly used excitation frequency but also other design parameters of interest. In numerical simulations, a two degrees of freedom system and a lumped parameter bladed-disk model with dry friction dampers are employed to validate the effectiveness and stability of the method. Meanwhile, the effects of damper design parameters on the responses are investigated, especially the effect of normal force is studied to find the optimal solution. The results indicate that the proposed analytical method can provide an accurate quantitative assessment for the optimum design of the bladed-disk dampers.

This paper presents a study on the nonlinear dynamic behavior of a stiffened plate with the existence of initial stresses. A stiffened plate is assumed to be composed of a plate and some stiffeners, which are treated separately. The plate is analyzed based on Thin Plate Theory, while the stiffeners are considered as geometrically nonlinear Euler-Bernoulli beams. The equations of both kinetic energies and strain energies of the plate and stiffeners are established. After that, the dynamic equilibrium equations for the stiffened plate are derived according to Lagrange equation. The nonlinear frequency for single-mode result is obtained through Elliptic function, and the accuracy of the analytical solution is verified through comparison with Ansys finite element method. In addition, homotopy analysis method is used to solve 3:1 internal resonance of the stiffened plate. With parametric analysis being conducted, the investigation on how initial stresses influence the nonlinear dynamic properties is carried out. Some useful nonlinear dynamic properties and conclusions are obtained, and thees can provide references for engineering application.

In this paper, the modal coupling mechanism is studied of a single-span footbridge consisting of a suspended beam (i.e., bridge deck), two suspension cables (via hangers) and two wind guys (via wind ties). To start, the governing equations for the slender suspended beam are derived based on the linearized deflection theory for classical suspension bridges, which is followed by two parts. First, the free vibration analysis is conducted to obtain the modal frequencies and modal shapes of the suspended beam by Galerkin’s method, from which the key parameters dominating the flexural-torsional coupled vibrations are identified, along with measures for stiffness enhancement. Then, a virtual eccentrically moving vehicle is first attempted to scan (i.e. extract) the vibration messages of the suspended beam from a perspective that allows us to physically interpret the dominant mode of the flexural-torsional coupling of the beam in an easy way. The objective of this study is twofold: first to offer a complete nonlinear vibration theory for the suspension footbridge, and second to physically interpret the complicated mechanism of coupling involved.

International audience; Motivated by the current demands in high-performance structural analysis, and by a need to better model systems with localized nonlinearities, analysts have developed a number of different approaches for modeling and simulating the dynamics of a bolted-joint structure. However, it is still unclear which approach might be most effective for a given system or set of conditions. To better grasp their similarities and differences, this paper presents a numerical benchmark that assesses how well two diametrically differing joint modeling approaches – a time-domain whole-joint approach and a frequency-domain node-to-node approach – predict and simulate a mechanical joint. These approaches were applied to model the Brake-Reuß beam, a prismatic structure comprised of two beams with a bolted joint interface. The two approaches were validated first by updating the models to reproduce the nonlinear response for the first bending mode of an experimental Brake-Reuß beam. Afterwards, the tuned models were evaluated on their ability to predict the nonlinearity in the dynamic response for the second and third bending modes. The results show that the two joint modeling approaches perform about equally as well in simulating the Brake-Reuß beam. In addition, the exposition highlights improvements that were made in each method during the course of this work and reveal further challenges in advancing the state-of-the-art.

In this paper, an efficient numerical method consisting of the real mode component mode synthesis (CMS) model reduction, shooting method with parallel computing, and Floquet analysis was developed for nonlinear rotordynamics analysis of a flexible rotor supported by a four-lobe flexure pivot tilting pad journal bearing (FPTPJB) in load-on-pad (LOP) and load-between-pad (LBP) orientations in comparison to a fixed profile journal bearing (JB) of the same pad geometry. The method used the rotor's finite elements and bearing forces obtained from directly solving the Reynolds equation to determine the limit cycles and Hopf bifurcation types. For the investigated rotor and bearing parameters, the numerical results indicated that the onset speed of instability (OSI) of FPTPJB is considerably higher than that of JB of the same orientation. Also, FPTPJB in LOP orientation yielded substantially higher OSI than the LBP one, whereas the OSI of JB in LOBP orientation was higher than the LOP counterpart. Nonlinear calculation results indicated that all bearing types and orientations gave subcritical Hopf bifurcation. The FPTPJB in LOP orientation produced the largest stable operating region, whereas the JB in LBP configuration yielded the smallest one. The experiment showed subcritical Hopf bifurcation occurred at speed close to the calculated OSI in all cases except FPTPJB in LOP orientation that the OSI is higher than the maximum test rig speed. The whirling orbit had the same frequency as the first critical speed and was precessed in the shaft rotation direction.

Made available in DSpace on 2021-06-25T10:17:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-05-01 In some applications, such as ground vibration testing in the aerospace industry, it is of interest to observe the modal behaviour of a slender structure while it is statically loaded. One way of statically loading such a structure is to suspend masses using very soft springs. If the springs are linear, then this results in an extremely large static deflection of the springs. This problem could be overcome by dynamically isolating the masses using quasi-zero stiffness (QZS) springs. This paper describes the design, construction and experimental testing of a device that can exhibit QZS. A novel design is proposed that allows the stiffness and the symmetry of the device to be adjusted independently using separate adjustment mechanisms. Quasi-static and dynamic testing of the device show that it can be adjusted to have an extremely low stiffness within the limits of measurement. The main trend of the force-displacement curve shows that it has a cubic stiffness characteristic, and that friction is responsible for its hysteretic behaviour. Dynamic testing shows that the device locks-up due to friction at low frequencies, but at high frequencies the device acts as an efficient linear isolator. An experiment was also performed where a mass was suspended on a multi-modal beam structure via the QZS device. It was shown that a static load could be applied to the beam without the attached mass appreciably affecting the dynamic response of the beam, even though the suspended mass was about 12% of that of the host structure. College of Engineering Swansea University Department of Mechanical Energy and Management Engineering University of Calabria Department of Mechanical Engineering Faculty of Engineering UNESP Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education Dalian University of Technology Department of Mechanical Engineering Faculty of Engineering UNESP

A metastructure plate featuring periodically embedded nonlinear vibration absorbers (NVAs) is proposed for the passive suppression of nonlinear aeroelastic responses under supersonic flow conditions. Using the von Karman large deformation theory and supersonic piston theory, the motion equations of a supersonic functionally graded material plate coupled with NVAs are derived from the Hamilton principle. Linear flutter analysis shows that the multiple-NVA design can significantly enhance the aerothermoelastic stability of the metastructure plate. Subsequently, the nonlinear aeroelastic behaviors of the plate and the energy transfer mechanism between it and the NVAs are examined using an energy-based analysis approach. The comparison of bifurcation diagrams indicates that the attachment of periodic NVAs realizes a superior suppression of vibration absorption than a single NVA. Numerical results show that the nonlinear dynamic responses of the plate can be substantially reduced via the targeted energy transfer of NVAs in the post-flutter regime. In particular, the passive control performance of the periodic NVAs does not degrade under an increase in the dynamic pressure. Furthermore, a significant reduction of more than 95% in the response amplitude of the plate can be realized by properly tuning the NVA parameters. The present work demonstrates that the metastructure design, based on periodically distributed NVAs, is effective at enhancing the flutter stability and mitigating nonlinear aeroelastic responses.

Abstract This paper investigates two parameters effect on vibrational responses of the spiral bevel gear. Changing the gear system overall stiffness (GSOS) considering elastic deformation and periodic torques are the two parameters which are represented as the main goals of this study. In order to investigate the effects of shaft stiffness and elastic deformation, two different cases with different support locations are considered. The first case is presented by locating the support close to the gear, and in the latter one, the distance between gear and support is increased. Besides, to study the effect of torque, two main types are considered: constant and periodic excitation torque. To illustrate the dynamic behavior, the governing differential equations are solved numerically according to the Runge–Kutta method. The equations are nonlinear due to backlash and time-varying coefficients as the results of GSOS variation. Vibrational phenomena are illustrated by means of bifurcation diagrams, RMS, and Poincaré maps. Particular vibrational behaviors such as “chaos” and “period-doubling” phenomena are illustrated with details. By investigating the effect of shaft stiffness, results show that when the support is far away from gear, the vibration response increased by 67.5%. Moreover, while the input torque is constant, the support movement does not cause undesirable responses such as chaotic or period-doubling responses. The periodic torque causes undesirable responses such as chaos and bifurcation and period-doubling responses. Article Highlights What is done in the present paper can be mentioned in three main parts: The nonlinear dynamics of the spiral bevel gear pair under two different support situations is investigated in this paper. To scrutinize the dynamic behavior of the spiral bevel gear-pair in a nearly real situation, the input driver torque is periodically variable. The results show that the spiral bevel gear pair may comprise chaotic response with periodic torque excitation if the bearing supports locate far enough from the gears.

The nonlinear dynamic response of an imperfect beam resting on elastic foundation has received a great deal of attention in the last decade due to their promising functionality and features.

In this paper, the dynamic model of a pre-twisted cracked rotating blade is established using self-programed beam element (CBE) and its nonlinear characteristics are analyzed. Firstly, based on the Castigliano’s theorem, the CBE with an open crack model is established. Secondly, a new breathing model of CBE is proposed in terms of the change of the crack contact region. Subsequently, the finite element (FE) model of a pre-twisted cracked rotating blade is established, and then verified by the ANSYS model. Finally, the effects of the crack depth, the crack position, the aerodynamic amplitude and the rotating speed on blade vibration characteristics and crack breathing status are investigated. The results show that the proposed model relative to the ANSYS model is of high efficiency and accuracy, besides, the larger crack depth and higher rotating speed result in a non-breathing crack, while the larger crack position and aerodynamic amplitude result in a breathing crack.

There are complex nonlinear behaviors and mechanisms in the bolted joint interface. Thus, the bolted joint is crucial to the complex nonlinear dynamic response of the structure. However, in the traditional structural dynamic analysis, the screw connection is usually neglected, which makes it challenging to analyze and study the nonlinear dynamic behavior of bolted structures. Hence, based on the Timoshenko beam theory and finite element method, this paper introduces a model considering thread connection to analyze the dynamic response under different excitation. Eventually, the results indicate that owing to the local nonlinearity of bolts, the whole bolted cantilever beam shows hardening-type characteristics. In addition, the frequency response curve also depicts the typical nonlinear phenomenon of instability and uncertainty, namely bifurcation, which preliminarily verifies the correctness and accuracy of the bolted cantilever beam model.

In this study, the nonlinear vibration (bifurcation type) of a highly flexible rotor supported by a journal bearing (JB) and self-aligning rolling element bearing (REB) under various configurations of rotor large disk mass/position, bearing length-to-diameter (L/D) ratio, and preload was investigated using two different bearing models: the model that considers both lateral and angular motion (Model A) and the model that considers just lateral motion (Model B). The rotor was modelled by 1-D finite elements (FE), and its degrees-of-freedom (DOF) was reduced to the DOF of the JB’s node by real mode component mode synthesis (CMS). Then, the shooting method and arclength continuation were applied to the reduced rotor model to obtain nonlinear limit cycles. Also, parallel computing was applied to the shooting method to shorten the calculation time. The stability of the obtained limit cycles was then determined by Floquet multiplier analysis. The experiment on the test rig with the same rotor and bearing parameters utilized in the calculation was carried out to verify the bearing models in each configuration. The calculation and experimental results showed that the bifurcation type calculated by Model A agreed with experimental results in all configurations. In addition, if the L/D ratio was short or the large disk position was near the rotor midspan, the bifurcation type obtained from both Model A and B agreed with the experimental results. The discrepancy in bifurcation type obtained from both bearing models only occurred in the cases that the L/D ratio was long and the large disk position was near the JB. Lastly, decreasing the L/D ratio, increasing preload, and moving the large disk position closer to the JB tended to change the bifurcation type from subcritical to supercritical.

Turbine blades are now being used under increasingly severe conditions in order to increase the thermal efficiency of gas turbines. Friction dampers are often used to reduce the vibration of the blade and improve the plant reliability. This is a general study dealing with resonance passing where the natural frequency of the turbine blade coincides with the frequency of specific harmonic excitation forces while increasing the turbine rotation speed. Asynchronous components of excitation forces are also considered in addition to the synchronous components caused by specific harmonic excitation forces. In this study, a new method for predicting the characteristics of nonlinear vibration under excitation force including both synchronous and asynchronous force components is developed. In order to investigate the effect of additional asynchronous loading, time history response analyses considering nonlinear vibration using simulated turbine blades were conducted. Results showed that friction damper slip can be induced by the presence of the additional asynchronous excitation force components even for low values of synchronous excitation force. It is shown that it is possible to use a calibration factor to predict vibration characteristics considering friction slipping by estimating the ratio of the total excitation force to the single harmonic excitation force. To verify the effect of asynchronous excitation force and the validity of the proposed correction method, verification tests were conducted experimentally. The experimental results show that friction slipping occurred under small harmonic excitation force when there was asynchronous excitation force and show good agreement with the numerical results. Moreover, the validity of the proposed method which corrects the dynamic characteristics obtained using of the first order harmonic balance method is confirmed.

The effect of bearing length to diameter (L/D) ratio and large disk position on nonlinear vibration (limit cycle and bifurcation type) of a flexible rotor-bearing system is investigated. The rotor consists of a shaft modeled by 1-D finite elements (FE), two small disks and a large disk. It is supported by a self-aligning ball bearing and an axial-groove journal bearing with L/D ratio of 0.4 and 0.6. Two large disk positions: 340 and 575 mm measured from the ball bearing are investigated. The journal angular motion, which is essential for the highly flexible rotor but typically not considered in the previous nonlinear vibration literature; is considered in nonlinear bearing force calculation. The degrees of freedom (DOF) of the rotor-bearing system are reduced to those of the node that the nonlinear journal bearing force and moment act on by real mode component mode synthesis (CMS) that retains only the 1st forward and backward modes. Shooting method and Floquet multiplier analysis are applied to the reduced rotor-bearing system to obtain limit cycles and their stability of each bearing L/D ratio and large disk position case. Numerical results indicate that supercritical Hopf bifurcation only occurs in the case of L/D = 0.4 and large disk position 575 mm, otherwise subcritical occurs. However, if the typical bearing model that does not consider journal angular motion is used, the bifurcation type for the case of L/D = 0.6 with large disk position 575 mm will change to supercritical. Lastly, the experiments with the same L/D ratio and large disk position investigated in the calculation are performed as a validation. The experimental result of each case shows the same bifurcation type as the calculation result using the bearing model that considers the journal angular motion.

This work investigates the primary resonance and internal resonance of a double-section beam with cubic nonlinearities. This model can be applied in a wide range of engineering problems, such as rocket and missile structures. Even space technology has been developed for decades; several nonlinear properties deserve further study, especially, for the internal resonance. The method of multiple scales (a perturbation technique) is employed to analyze this nonlinear problem. This study focuses on finding the forcing conditions of this 3D double-section beam to trigger the often-ignored internal resonance or prime resonance in rocket structures. A primary resonance is found on a uniform free-free beam at certain flight speed. The three-to-one internal resonance of the double-section beam occurs within the first and the second modes in the diameter ratio of 1/0.75 with the length ratio of 0.33 or 0.51. The semi-analytical results are verified by the time marching numerical method.

In this study, different alternatives to detect and localize damage from linear and nonlinear vibration responses were investigated. These alternatives were compared on two concrete slabs subjected to different damage extents. Linear and nonlinear modal test configurations were considered. The variations of linear resonant frequencies, modal assurance criterion values, and nonlinear hysteretic parameters were used to detect damage. Then, the modal shapes were used to locate damage positions. The maximum principal curvatures derived from the original modal shape displacements between damaged and undamaged states made it possible to spot the damaged zones. Damage localization was further enhanced by weighting the principal modal shape curvature differences for every mode by their respective variations of the nonlinear hysteretic parameter. Finally, damage localization was achieved using different outlier identification techniques.

In recent years, great advances in understanding the opportunities for nonlinear vibration energy harvesting systems have been achieved giving attention to either the structural or electrical subsystems. Yet, a notable disconnect appears in the knowledge on optimal means to integrate nonlinear energy harvesting structures with effective nonlinear rectifying and power management circuits for practical applications. Motivated to fill this knowledge gap, this research employs impedance principles to investigate power optimization strategies for a nonlinear vibration energy harvester interfaced with a bridge rectifier and a buck-boost converter. The frequency and amplitude dependence of the internal impedance of the harvester structure challenges the conventional impedance matching concepts. Instead, a system-level optimization strategy is established and validated through simulations and experiments. Through careful studies, the means to optimize the electrical power with partial information of the electrical load is revealed and verified in comparison to the full analysis. These results suggest that future study and implementation of optimal nonlinear energy harvesting systems may find effective guidance through power flow concepts built on linear theories despite the presence of nonlinearities in structures and circuits.

Due to the quasi-zero-stiffness and overload protection characteristics, constant-force mechanisms can be widely used in nonlinear vibration control, high-efficiency shock isolation, and other engineering fields. As a preparatory work for the further applications, this paper presents a cam-based constant-force compression mechanism and validates the quasi-static characteristics experimentally. By employing the friction considered profile identification method to design the cam and through the interaction between the cam and spring-sliders, the constant-force compression mechanism can passively output the desired constant force over a sufficiently large displacement. The design theory is firstly introduced in detail. Through establishing and solving the differential relationship between the lateral elastic force and vertical constant force, the constant-force compression mechanism under various frictional conditions can be designed. Then, constant-force compression mechanism prototypes corresponding to sliding and rolling friction are designed, fabricated and tested respectively. The results show that both the prototypes have the satisfactory characteristics as with the design requirements. Moreover, the relative generality and stronger engineering applicability of the proposed friction considered profile identification method are proved since it can not only cover the frictionless (micro-friction) cases, but keep the constant-force behavior of the constant-force compression mechanism under the nonignorable friction conditions. Therefore, compared with the existing cam-roller constant-force mechanisms that must ensure the ignoring micro-friction demand, the presented constant-force compression mechanism taking friction into consideration has important engineering significance since it can reduce this machining requirement.