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The progress made in the decade 1973–1983 in the area of vibration of jet engine blades is surveyed. The purpose of the survey is to provide a general review of recent progress and the limited number of references cited can be used to reach the many other important publications in this area. Both structural and aerodynamic aspects of blade vibration are discussed, although the emphasis is on the former. The areas of future analytical and experimental research needed to continue to influence the design of these components are outlined.

The aim of this paper is to apply and compare four reduced-order modeling strategies to compute the unbalanced vibration response of a rotating machine and evaluate its robustness to random matrix perturbation. The full finite element model of the rotor is built using a rotordynamic open source software (ROSS), and is reduced through different methods, namely: (1) modal reduction, (2) Krylov subspace, (3) Guyan reduction, and (4) System Equivalent Reduction-Expansion Process (SEREP). To evaluate the robustness of the obtained results, this paper proposes to perturb the stiffness matrix obtained using the reduced-order models applying the random matrix theory. A simple rotor (three discs) and a more complex gas turbine model (twenty-one discs) are analyzed. Results show that Guyan is not the most appropriate reduction technique for the systems analyzed, but the other three strategies yield good results. In addition, the same random perturbation in the reduced-order stiffness matrices produces a similar level of uncertainty on the stochastic unbalanced responses.

Dynamically substructured systems (DSS) are a typical technique to achieve real-time numerical simulations combined with physically tested components. However, the rigorous feasibility analysis before the implementation is missing. This paper is aimed to fill this gap by establishing rigorous conditions for when DSS is suitable for dynamic testing. The proposed method is based on novel symbolic recursive formulations for the transfer functions describing a generic lumped parameter vibrating structure, enabling the analysis of structural and other properties without requiring the computation of explicit symbolic expressions for the transfer functions involved, representing a significant breakthrough as it allows to perform feasibility analysis in analytical form, rather than solely relying on numerical approaches. The series of analytical conclusions presented in this paper, and future ones unlocked by the proposed approach, will significantly enrich the research in the community of DSS and structural vibrations. In particular, the proposed approach allows performing analysis of causality, controllability and observability using much reduced knowledge of the structure, thus significantly simplifying such analysis. Analytical conclusions on stability can also be made with the help of novel recursive form, removing the need of repeatedly calculating the roots of characteristic equations, a task that can be performed only via numerical approaches and for which analytical results are not available. The proposed methodology can be applied to a whole class of vibration problems and is not linked to any specific structure, going beyond the specific examples available in the literature.

Nonlinear dynamics analysis is a crucial topic in mechanical and aerospace engineering. The analysis of nonlinear normal modes (NNMs) provides an effective mathematical tool for interpreting complex nonlinear vibration phenomena. Unlike the invariant normal modes of linear systems, NNMs often exhibit frequency-energy dependence and cannot be computed using the traditional eigen-decomposition method. Calculating NNMs relies on numerical methods that involve expensive iterative computations, especially for systems with numerous degrees-of-freedom. To relieve computational costs, this paper proposes a mode selection method for the component mode synthesis (CMS) technique to enable compact reduced-order modeling of structures with localized nonlinearities. The reduced-order model is then combined with a numerical continuation scheme to establish a low-cost NNM analysis framework. This framework can efficiently predict the NNMs of high-dimensional finite element models. The proposed framework is demonstrated on an I-shaped cantilever beam with localized nonlinear stiffness. The results show that the proposed approach can identify the key modes in the CMS modeling procedure. The NNMs of the nonlinear I-shaped beam structure can then be analyzed with a significant reduction in computational costs.

Selecting the proper set of Degrees of Freedom is essential in inverse (Blocked) Force calculation. Including too many Degrees of Freedom in the computation can lead to overfitting, resulting in inaccurate force estimations and poor prediction quality. The discrepancy arises from errors within the dataset, such as measurement noise or other artifacts. This paper presents a solution to the overfitting problem, introducing the X-DoF procedure to automatically identify the relevant subset of Blocked Force Degrees of Freedom. Its effectiveness is showcased through numerical and experimental validation and compared against regularization techniques.

The genesis of clutch noise, encompassing squeaks, chatter, shudders, or judders, predominantly arises from friction-induced vibrations. As time progresses, the degradation of the clutch friction lining manifests due to diverse factors, such as the smearing of surface irregularities, elevated transmission fluid temperatures, fluctuating axial pressure, or aggressive shifting. Consequently, the slope of the friction curves tends to assume a negative gradient, giving rise to adverse damping effects like self-excited oscillations or stick-slip oscillations within the clutch pack. A lesser-discussed phenomenon, known as squawking, occurs through analogous mechanisms discussed in this paper. This paper delves into investigating the occurrence of squawking noise observed in automatic transmission multi-disc clutches during low-speed up-shifts. The study discerns friction-induced vibrations as the primary contributor to squawk during the inertia phase of the clutch engagement cycle, a facet previously unidentified. During this phase, high-frequency weakly damped oscillating modes become self-excited due to the negative slope of the coefficient of friction versus slip speed curve. The coefficient of friction functions as negative damping during the inertia phase, where the energy dissipation from damping is insufficient to completely halt the oscillations, allowing them to persist approximately at the natural frequency until clutch lock-up. Experimental data validate the proposed model and hypothesis, with results closely aligning with numerical simulations. The paper concludes by offering practical suggestions to prevent and mitigate squawk in automatic transmission wet clutches, with the aim of enhancing overall performance and reducing undesirable noise.

In this paper, a properly tuned vibration absorber (spring-mass system) is used to induce a point of zero vibration, or node, anywhere along an arbitrarily supported beam for the purpose of suppressing vibration. Other benefits of enforcing a node include the ability to place a sensitive instrument near or at a point where there is little or no vibration, and to keep any point along the beam stationary without using a rigid support. The assumed-modes method is used to discretize the equations of motion, which conveniently leads to the beam displacement at the node location in matrix form. Exploiting the Sherman-Morrison inverse formula, one can obtain compact, closed-form expressions for the beam deflection at the node location and the displacement of the absorber mass, explicitly in terms of the absorber parameters, attachment location, excitation frequency, forcing location and the node location. The resulting expressions can then be used to systematically perform a parameter sensitivity analysis and rapid design modifications. The proposed work contributes to the parametric study of Euler-Bernoulli beams by leveraging closed-form sensitivity expressions to rapidly account for inverse problems involving parameter tolerances and perturbations. The method introduced in this paper can also be easily extended to accommodate changes in attachment location and the tolerable deflection of the absorber mass without the need to perform a potentially expensive and time-consuming re-analysis. Numerical examples are presented to illustrate the utility of using the sensitivity expressions in designing an accurate and robust vibration absorber when slight modifications are introduced.

In the field of rail transport and aerospace field, vibration energy harvesting is inevitably subjected to coupled excitations, including train wheel–track interaction induced friction heat and forced vibration, periodic thermal radiation, and vibration excitation. This paper investigates a coupled thermo-electric-elastic piezoelectric vibration energy harvester with axial movement under external heat flux and mechanical force load. The coupled forced vibration equation, coupled electric equation, and coupled thermoelastic heat conduction equation are derived and solved by Green's function theory. To analyze the effect of excitations on the response characteristics, the decoupled method is utilized to solve the coupled multi-field equations and obtain the displacement, electric, and temperature distribution closed-form solutions. The displacement coupling effect induced temperature distribution and the thermo-electric coupling effect triggered displacement are respectively decoupled and analyzed. The obtained closed-form temperature distribution and displacement solutions are verified by the finite element method. To further verify the obtained solutions, a numerical method is conducted by decoupling the coupled multi-field equations and comparing them with prior solutions. Additionally, the different height-to-length ratios, axially moving speeds, and external force load are analyzed in detail. The results indicate that the displacement, temperature distribution, and output voltage vary with external conditions due to the coupled multi-field effect. Overall, this work investigates the thermo-electric-elastic coupling effect on the axially moving piezoelectric energy harvesting, which is beneficial to promote theoretical investigations of the coupled multi-field energy harvesting system and accelerate the practical applications in the aerospace field.

Tire/road noise is one of the major sources of noise pollution in urban areas. This phenomenon can be described as the combined effect of several generation and amplification mechanisms. Acoustic resonances due to the tread grooves at the footprint region, also known as pipe resonances, are particularly important since they can generate high noise levels if they combine with harmonic generation mechanisms. This paper deals with a numerical investigation of this phenomenon and describes modeling approaches that might be used to estimate the frequencies and the mode shapes of these resonances.

Mechanical shock events experienced by electronic systems can be reproduced in the laboratory using Hopkinson bar tests. In such tests a projectile strikes a rod, creating a pulse which then travels into the electronic system. The quality of these tests depends on the closeness of the shape of the incident pulse to a desired shape specified for each test. This paper introduces a new approach for controlling the shape of the incident pulse through the use of phononic material concepts, thereby improving the test procedure. Two dispersion-modifying concepts, phononic crystals and local resonators, are examined for their wave shaping capabilities in one-dimensional elastic waveguides. They are evaluated using a transfer matrix method to determine the output pulse shape in the time domain. Parametric studies show that no single parameter allows for precise-enough control to achieve the possible desired output pulse shapes. Instead, the parameters of an approximate, discrete model for a combined phononic crystal/locally resonant system are optimized together to achieve the desired pulse shape. A sensitivity analysis documents that the pulse shape is relatively insensitive to errors in the optimized parameter values. The optimized discrete model is then translated into a physical design, which when analyzed using the finite element method shows that desired pulse shapes are indeed produced.

By exchanging the internal energy between coupled vibration modes, internal-resonance-based energy harvesters may provide an effective solution to broadening and enhancing bandwidth and power performance in dealing with natural vibration sources. With the development of piezoelectric-based transducers, thickness and face shear coefficients in proper piezoelectric elements can also generate the power output from shear deformation on the core vibrating elements. However, in most cantilever-based energy harvesters that focused on bending modes, the shear responses were neglected. In this paper, we present an internal-resonance-based piezoelectric energy harvester with three-dimensional coupled bending and torsional modes, for the first time. The fine-tuned system leverages a two-to-one internal resonance between its first torsion and second bending modes to enhance the power output with piezoelectric effects. The dynamic behaviour implies the coexistence of in-plane and out-of-plane motions under a single excitation frequency, and the corresponding strain changes in the bending and shear directions are captured by bonded piezoelectric transducers. Dependence between excitation levels and the internal-resonance phenomenon is justified as a critical system parameter study; the results also indicate that an intriguing non-periodic region exists near the centre frequency. The outcomes of this study feature a multi-directional and multi-modal energy harvester that displays rich dynamic behaviors. The operational bandwidth is promising for broadband energy harvesting, and the output voltage is enhanced by capturing both in-plane and out-of-plane motions at the same time.

The traveling and standing flexural waves in the micro-beam are studied based on the fraction order nonlocal strain gradient elasticity in the present paper. First, the Hamilton's variational principle is used to derive the governing equations and the boundary conditions with consideration of both the nonlocal effects and the strain gradient effects. The fraction order derivative instead of the integer order derivative is introduced to make the constitutive model more flexible while the integer order constitutive model can be recovered as a special case. Then, the Euler-Bernoulli beam and the Timoshenko beam are both considered and the corresponding formulations for them are derived. Two problems are investigated: 1) the dispersion of traveling flexural waves and the attenuation of the standing waves in the infinite beam. 2) The natural frequency of finite beam. The numerical examples are provided and the effects of the nonlocal and the strain gradient effects are discussed. The influences of the fraction order parameters on the wave motion and vibration behavior are mainly studied. It is found that the strain gradient effects and the nonlocal effect have opposite influences on the wave motion and vibration behavior. The fraction order also has evident influence on the wave motion and vibration behavior and thus can refine the prediction of the model.

In this paper, a hybrid mass damper (HMD) and its hyperstability thanks to a power flow approach are studied. The HMD proposed combines an active control system with an optimal passive device. The initial passive system is an electromagnetic Tuned Mass Damper (TMD) and the control law is a modified velocity feedback with a phase compensator. The resulting hybrid controller system is theoretically hyperstable and ensures fail-safe behavior. Experiments are performed to validate the numerical simulation and provide good results in terms of vibration attenuations. Both excitation from the bottom in the frequency domain and shock response in the time domain are tested and analyzed. The different power flows in terms of active and reactive powers are estimated numerically and experimentally on the inertial damper (passive and active) and on the HMD. More over, through a mechanical analogy of the proposed system, it is shown that this hybrid device can be seen as an active realization of an inerter based tuned-mass-damper associated with a sky-hook damper. Observations and analysis provide insight into the hyperstable behavior imposed by the specific control law.

A previously proposed planar axisymmetric dynamic vibration absorber (DVA), with embedded acoustic black hole (ABH) features, has been shown to suffer from the very selective coupling with the host structure, thus compromising its vibration reduction performance. To tackle the problem, an eccentric ABH-based circular DVA whose thickness profile is tailored according to a circumferential gradient variation is proposed in this paper. This new configuration preserves the ABH profile in the radial direction alongside a continuous variation along the circumferential direction and breaks the axisymmetry of the original DVA design at the same time. While the former permits the ABH features to fully play out in a continuous manner, the later entails a more effective coupling with the host structure. These salient properties have been demonstrated and confirmed both numerically and experimentally by examining a benchmark plate structure. For analyses, a coupling model embracing the host structure and the add-on DVAs is established which allows the calculation of the coupling coefficient, a vital quantity to guide the DVA design. Studies demonstrate the advantages of the proposed DVA over existing designs for the same given mass. The enriched structural coupling and the enhanced modal damping, arising from the eccentric and circumferentially graded ABH design, are shown to be the origin of such improvement. All in all, the physical process underpinning the dynamic absorber principle and waveguide absorber from the host structures is simultaneously consolidated, thus leading to superior broadband structural vibration suppression.

This study investigates the theoretical and experimental aspects of the vibro-acoustic characteristics of cylindrical shells with internal substructures. On the theoretical side, a hybrid calculation method is proposed, which combines the condensed transfer function method with the direct stiffness method and the precise transfer matrix method. The cylindrical shell with internal substructures is decoupled, and the governing equations for the cylindrical shell substructure and the internal substructure are separately established. Furthermore, the coupling forces between the cylindrical shell substructure and the plate substructure are solved based on the condensed transfer function method. These coupling forces are then incorporated into the overall transfer equation of the cylindrical shell to obtain the vibro-acoustic response of the coupled structure. Compared with the finite element calculation results, the validity of the calculation method in this paper is verified. In terms of experiments, the natural frequency, mode, and vibration acoustic response of the model were tested and compared with the theoretical results, which was in good agreement. The study demonstrates that the proposed hybrid calculation method based on the condensed transfer function is effective in predicting the vibro-acoustic characteristics of cylindrical shells with internal substructures.

Vibrations due to tire–road contact in wheeled vehicles induce acoustic discomfort especially beyond 35 km/h. This paper proposes an active control method to reduce the vibration transmission from the tire–road contact to the vehicle through piezoelectric transducers located directly on the wheel spokes. Our approach relies on a double spatial modal filter to physically focus the control energy on the wheel pumping mode while avoiding any spillover phenomena. In addition, a bandpass controller ensures maximum damping on the targeted mode. The proposed control strategy is applied first to the clamped wheel in order to validate the static performance of the spatial controller. Then the wheel is excited through the tire and the efficiency of the controller is evaluated through the measured force passing by the wheel hub. Finally, the tire–wheel assembly (TWA) is placed on an experimental setup recreating the vehicle operating conditions with wheel rotation at different velocities and road excitations. The experimental results confirm the efficiency of the proposed control method and its robustness to the dynamics evolution of the structure in function of the TWA angular velocity.

In this paper, vibration analysis of rotating combined thin-walled shells with multiple conical segments has been carried out. Considering the centrifugal force, Coriolis force, and initial hoop tension due to rotation, the elastic strain energy and kinetic energy of a single rotating conical shell are expressed based on Love’s first approximation theory. The artificial springs are introduced to simulate the connections of adjacent conical shells and the boundaries of the rotating combined thin-walled shells. Taking characteristic orthogonal polynomial series as the admissible functions, the Rayleigh–Ritz method is employed to derive the frequency equations of the combined shell and corresponding vibration characteristics are then obtained. Given that the cylindrical shell and annular plates can be regarded as conical shells with semi-vertex angles of 0 deg and 90 deg, respectively, the solution given is also available for the vibration analysis of rotating combined thin-walled shells comprised of any segments of cylindrical, conical shell, and annular plate. As examples of rotating combined thin-walled shells with two and five segments, vibrations of rotating conical–conical joined shell and cylindrical–conical–cylindrical–conical–cylindrical joined shell are investigated in the paper. Traveling wave frequencies and corresponding mode shapes are shown, and the effects of rotating speed, circumferential wave number, spring stiffness, and semi-vertex angles on the vibration behavior are given in detail.

This paper presents the vibroacoustic response of pure functionally graded plates under transient loading of mechanical nature. The functionally graded plate is modelled using the conventional first-order shear deformation theory to incorporate the effects of transverse shear and rotary inertia. The mid-surface variables are determined using the finite element method. Transient structural response is determined using Newmark Beta time marching scheme and the acoustic pressure in the free field is obtained using the time-domain Rayleigh integral. The effective material properties of the FG plate and the transient response of both the structural and acoustic fields have been computed in MATLAB. The influence of the volume fraction index, thickness ratio and boundary conditions of pure FG plate on its transient vibroacoustic response is investigated by a detailed parametric study.

This paper aims to investigate the free coupled flexural-torsional vibrations of a double cantilever structure. The structure consists of two identical Euler-Bernoulli cantilever beams with a piezoelectric layer on top. The beams are connected by a rigid tip connection at their free ends. The double cantilever structure in this study vibrates in two distinct modes: flexural mode or coupled flexural-torsional mode. The flexural mode refers to the in-phase flexural vibrations of the two cantilever beams resulting in translation of the tip connection, while the coupled flexural-torsional mode refers to the coupled flexural-torsional vibrations of the cantilever beams resulting in rotation of the tip connection. The latter is the main interest of this research. The governing equations of motion and boundary conditions are developed using Hamilton's principle. Two uncoupled equations are realized for each beam: one corresponding to the flexural vibrations and the other one corresponding to the torsional vibrations. The characteristic equations for both the flexural and the coupled flexural-torsional vibration modes are derived and solved to find the natural frequencies corresponding to each mode of vibration. The orthogonality condition among the mode shapes is derived and utilized to determine the modal coefficients corresponding to each mode of vibration. Moreover, the analytical and experimental investigations show that the coupled flexural-torsional fundamental frequency of the structure is dependent on dimensional parameters including the length of the cantilever beams and the length of the tip connection.

The first-passage time probability plays an important role in the reliability assessment of dynamic systems in random vibrations. To find the solution of the first-passage time probability is a challenging task. The analytical solution to this problem is not available even for linear dynamic systems. For nonlinear and multi-degree-of-freedom systems, it is even more challenging. This paper proposes a radial basis function neural networks method for solving the first-passage time probability problem of linear, nonlinear, and multi-degree-of-freedom dynamic systems. In this paper, the proposed method is applied to solve for the backward Kolmogorov equation subject to boundary conditions defined by the safe domain. A null-space solution strategy is proposed to deal with the boundary condition. Several examples including a two degrees-of-freedom nonlinear Duffing system are studied with the proposed method. The results are compared with Monte Carlo simulations. It is believed that the radial basis function neural networks method provides a new and effective tool for the reliability assessment and design of multi-degree-of-freedom nonlinear stochastic dynamic systems.

In this paper, the nonlinear response of indenter–foam dampers is characterized. Those dampers consist of indenters pressed on open-cell foams swollen with wetting liquids. Recently, the authors identified the dominant mechanism of damping in those dampers as poro-viscoelastic (PVE) relaxations as in articular cartilage, one of nature’s best solutions to vibration attenuation. Those previous works by the authors included dynamic mechanical analyses of the indenter–foam dampers under small vibrations, i.e., linear regime. The current study features the dynamic response of similar dampers under larger strains to investigate the nonlinear regime. In particular, the indenter–foam dampers tested in this paper consist of an open-cell polyurethane foam swollen with castor oil. Harmonic displacements are applied on the swollen and pre-compressed foam using a flat-ended cylindrical indenter. Measured forces and corresponding hysteresis (force–displacement) loops are then analyzed to quantify damping performance (via specific damping capacity) and nonlinearities (via harmonic ratio). The effects of strain and strain rates on the damping capacity and harmonic ratio are investigated experimentally. The dominant source of the nonlinearity is identified as peeling at the indenter–foam interface (and quantified via peeling index). A representative model consisting of a linear viscoelastic foam and rate-dependent adhesive interface (slider element with limiting adhesive strength) explains the observed trends in peeling and thus nonlinear dynamic response. Possible remedies to suppress those nonlinearities in future designs of indenter–foam dampers are also discussed.

Manufacturing tolerances and engine wear produce slight variations in the nominally identical blades of a bladed disk, or blisk. In theory, the vibrational energy of a tuned blisk is evenly distributed among the identical blades. Mistuning arises when blades are not exactly identical, producing vibration localization at one or more blades that can lead to premature failure via high-cycle fatigue. Blisk designers must consider how expected manufacturing variations and potential engine wear affect blade vibration and lifetime. However, a single experimental blisk can only capture a single mistuned configuration, making experimental assessment of mistuning both cost- and time-prohibitive. This paper investigates piezoelectric-induced stiffness perturbations as a potential approach that enables rapid testing of a wide range of mistuned configurations in a lab environment. Integrating piezoelectric material onto the blisk produces a continuous range of effective blade stiffness values. Piezoelectric stiffness perturbations alter the relative stiffnesses of all blades, changing the mistuned configuration. Simulations of a lumped blisk model characterize piezoelectric mistuning to motivate use in experimental preliminary testing of blisks. Optimization of the piezoelectric stiffness perturbation enables testing of desired mistuned amplitude distributions. Finally, benchtop testing of an academic blisk validates the ability of piezoelectric stiffness perturbations to change the mistuned configuration without any mechanical adjustments. Overall, piezoelectric mistuning enables rapid investigation of a theoretically infinite number of mistuned configurations with only one experimental blisk.

Resilient elements are widely applied for vibration and noise control in many areas of engineering. Their complex dynamic stiffness gives fundamental information to describe their dynamic performance and is required for predicting structure-borne sound and vibration using dynamic modeling. Many laboratory measurement methods have been developed to determine the dynamic properties of resilient elements. This paper presents a review of recent developments in the measurement methods from the perspective of force–displacement relations of the resilient element assembly rather than of their material properties. To provide context, the review begins with an introduction to modeling methods for resilient elements, especially for rubber and rubber-like isolators, and three standardized measurement methods are introduced. Recent developments are then discussed including methods to extend the frequency range, which are mainly developments of the indirect method. Mobility methods, modal-based methods, recent active frequency-based substructuring (FBS), and inverse substructuring (IS) methods to study the dynamic properties of resilient elements are also described. Laboratory test rigs and the corresponding identification methods are outlined. Methods to evaluate nonlinear dynamic properties of resilient elements by laboratory measurements are also discussed. Finally, the review is concluded by discussing the advantages and limitations of the existing methods and giving suggestions for future research.

Presently, passive methods of controlling combustion instability fall short when one considers stabilizing multiple acoustic modes. In this paper, we present a passive control approach based on the locations of the burners to stabilize multiple acoustic modes. The approach is demonstrated using linear stability analysis performed on a canonical open–open rectangular tube enclosing a flame. A linear flame model based on the kinematic description of the flame surface is used. A simultaneous solution method, as opposed to a segregated method, is developed to calculate the mean flow and to evaluate mode shapes and eigenvalues. The stability analysis is performed both on single and on multiple-burner combustors. In the latter case, the axial and transversal arrangement of burners considered preserves the net volumetric heat release rate and exit temperature. The problem of stabilizing the first three acoustic modes is cast as a multi-objective optimization problem for both types of combustors using the location(s) of the burner(s) as decision variable(s). We show that the use of multiple burners markedly increases the stability of the first three modes while not disturbing the combustor design parameters.

This paper proposes a novel phononic crystal sandwich beam (PCSB) for low-frequency and broadband vibration suppression. The representative volume element (RVE) consists of two hourglass truss unit cells with the same span but different rod radii. After validating the modeling method, a model of the PCSB is established to calculate band structure and transmittance response, and the results show good agreement. It is found that the PCSB can open wider and lower band gaps compared to a traditional sandwich beam (TSB). The band-folding mechanism is applied. The PCSB breaks the spatial symmetry, becomes diatomic, and opens the folding points, finally leading to two band-folding-induced gaps. The experiment is conducted on the PCSB, and the vibration band gap property is confirmed. Subsequently, the impacts of geometric parameters on the PCSB’s band gaps are investigated in detail. Design guidelines for tuning the geometric parameters toward lower frequency and broadband band gap are provided based on the parametric study results. In addition, the higher-order band-folding strategy is proposed. It is shown that a multi-folding PCSB can produce more band gaps. However, through two examples, i.e., second-folding and third-folding PCSBs, it is known that simply increasing the folding order may not be effective and even could deteriorate the vibration attenuation ability. In summary, this work explores a general strategy for designing sandwich beams with low-frequency and broadband vibration suppression ability.

This paper presents a new design method based on a robust-control strategy in the form of a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control. To apply the robust control theory, we first present an equivalent expression that describes a passive TMD as an active TMD. Then, some LMI-based condition is derived that not only guarantees robust stability but also allows us to adjust the robust H∞ performance. In particular, this paper considers the transfer function from a seismic-wave input to structural responses. Unlike other methods, this method formulates the problem to be a convex optimization problem that ensures a global optimal solution and considers uncertainties of mass, damping, and stiffness of a structure for designing a TMD. Numerical example uses both a single-degree-of-freedom (SDOF) and 10DOF models and seismic waves. The simulation results demonstrated that the TMD that is designed by the presented method has good control performance even if the structural model includes uncertainties, which are the modeling errors.

This paper presents a new approach to predicting an incipient critical speed in a rotating shaft. Based on the classical governing equations of motion for an eccentric mass on a flexible shaft (the Jeffcott rotor model), the approach is centered on examining the behavior of small perturbations or random disturbances to infer the approach of a critical speed (resonance). Such disturbances, that may be based on intentional probing, or simply the result of naturally occurring fluctuations, cause small transients. It is the changing nature of these transients (as characterized by their associated eigenvalues) that is used to assess the proximity to a critical speed. In this paper, the material developed is based on analysis, but generating the data from simulations or experiments will be the next step. The approach is a kind of stress-test, conceptually not dissimilar to structural health monitoring and damage detection but here directed toward the lead-up to resonance.

In this paper, the free vibration of rubber matrix cord-reinforced combined shells of revolution under hydrostatic pressure is investigated by the precise transfer matrix method. Under hydrostatic pressure, deformation and stress are generated in the rubber matrix composite shell. Based on the deformation characteristics of the rope structure, the deformation of the shell under hydrostatic pressure is analyzed. The stress of the shell under hydrostatic pressure is included in the shell differential equation of motion in the form of pre-stress. Then considering the fluid-solid coupling boundary condition, the field transfer matrix of the fluid-filled spherical shell is obtained. By the continuous condition of the state vector of the shell and the transformation relationship of the coordinate system, the transfer matrices at the position of the ring-stiffener and the connection position of the cylindrical shell and spherical shell are derived, and then the whole free vibration equation of the fluid-filled combined shells of revolution is assembled, and the natural frequencies are obtained by the boundary conditions. Eventually, the accuracy and reliability of the proposed method are verified by the results of literature and simulation results. Effects of the structural parameters of the spherical shell, the distribution of the ring-stiffeners, and the hydrostatic pressure on the natural frequencies of the fluid-filled combined shells of revolution are also discussed. Results of this paper can provide reference data for future studies in the related field.

The inerter pendulum vibration absorber (IPVA) is integrated between a spar and an annulus floater using a ball-screw mechanism to study its wave energy conversion potential. Hydrodynamic stiffness, added mass, and radiation damping effects on the spar-floater system are characterized using the boundary element method. It is found that a 1:2 internal resonance via a period-doubling bifurcation in the system is responsible for nonlinear energy transfer between the spar-floater system and the pendulum vibration absorber. This nonlinear energy transfer occurs when the primary harmonic solution of the system becomes unstable due to the 1:2 internal resonance phenomenon. The focus of this paper is to analyze this 1:2 internal resonance phenomenon near the first natural frequency of the system. The IPVA system when integrated with the spar-floater system is shown to outperform a linear coupling between the spar and the floater both in terms of the response amplitude operator (RAO) of the spar and one measure of the energy conversion potential of the system. Finally, experiments are performed on the IPVA system integrated with single-degree-of-freedom system (without any hydrodynamic effects) to observe the 1:2 internal resonance phenomenon and the nonlinear energy transfer between the primary mass and the pendulum vibration absorber. It is shown experimentally that the IPVA system outperforms a linear benchmark in terms of vibration suppression due to the energy transfer phenomenon.

This paper focuses on free vibration of hemi-ellipsoidal shells with the consideration of the bending rigidity and nonlinear terms in strain energy. The appropriate form of the energy functional is formulated based on the principle of virtual work and the fundamental form of surfaces. Natural frequencies and their corresponding mode shapes are determined using the modified direct iteration method. The obtained results, which show a close agreement with previous research, are compared with those obtained based on the membrane theory. The effect of the support condition, thickness, size ratio, and volume constraint condition on frequency parameters and mode shapes is demonstrated. With the bending rigidity, shell thickness has a significant impact on the frequency, especially in higher vibration modes and in shells with a considerable thickness but the frequency parameter converges to that determined by using the membrane theory while the reference radius-to-thickness ratio is increasing. In addition, accounting for the bending rigidity solves the issue of determining natural frequencies and mode shapes of the shells using the membrane theory without the volume constraint condition. The obtained results also indicate that the free vibration analysis with bending is essential for the hemi-ellipsoidal shell with a base radius-to-thickness ratio of less than 100, which gives over 2.84% difference compared with that of the shell derived by membrane theory, and this allows engineers to perform the analysis in more applications.

This paper addresses the experimental analysis of different stator configurations of an electric motor typically used within the automotive sector. The ongoing electrification of the automotive sector, combined with a desire to increase virtual prototyping, means that engineers are increasingly facing new challenges. Against this background, the numerical models of electric motors, particularly stators, are simplified and homogenized. However, this procedure must be supplemented by experimental data to ensure the high quality and reliability of the simulations. Unfortunately, broad experimental investigations are time-consuming and expensive, underlined by the lack of corresponding literature. For this reason, four different stator configurations were investigated as part of the experimental modal analysis to highlight the influence of the stator lamination as well as the winding. The results provide the scientific community with a broad outline of how specific influences change modal parameters of each stator configuration. In particular, the results show that lamination significantly reduces axial stiffness. Highlights of the findings relate to the mode-dependent stiffness, mass, and damping influences due to the winding, with the influence of the stiffness deviating significantly from expectation. It was also found that the selected winding technology dominates the structural dynamic system characteristics. Therefore, it is advisable to include the manufacturing technology intended to be used for the lamination and the winding in the early simulative design phase to improve the model prediction quality.

This paper explores the addition of small stubs with anechoic terminations (termed herein “anechoic stubs”) as a means of damping and/or removing vibration modes from planar frame structures. Due to the difficulties associated with representing anechoic boundary conditions in more traditional analysis approaches (e.g., analytical, finite element, finite difference, and finite volume), the paper employs and further develops an exact wave-based approach, incorporating Timoshenko beams, in which ideal and non-ideal anechoic terminations are simply represented by a reflection matrix. Several numerically evaluated examples are presented documenting novel effects anechoic stubs have on the vibration modes of a two-story frame, such as eliminated, inserted, and exchanged mode shapes. Modal damping ratios are also computed as a function of the location and number of anechoic stubs, illustrating optimal locations and optimal reflection ratios as a function of mode number. Forced vibration studies are then carried out, demonstrating reduced, eliminated, and inserted resonance response.

In this paper, an advanced non-dimensional dynamic influence function method (NDIF method) for eigenvalue analysis of arbitrarily shaped two-dimensional acoustic cavities with the mixed boundary consisting of the pressure-release and rigid-wall boundaries is proposed. The existing NDIF method has the weakness of having to calculate the singularity of the final system matrix of an analyzed acoustic cavity in the frequency band of interest to obtain the eigenvalues of the cavity because the final system matrix is dependent on the frequency. The newly proposed NDIF method in this paper provides an efficient way to extract accurate eigenvalues and eigenmodes by successfully overcoming the above weaknesses. Finally, the validity and accuracy of the proposed method are shown through verification examples.

Concrete box girder bridges occupy over 80% of the total mileage of the Chinese high-speed railway. The box girder structure has many natural modes of low frequencies, which can be excited by a train passing at high-speed, generating low-frequency bridge noise. This paper is concerned with the prediction of such bridge noise and reports a prediction model. The model, as other existing models of the same nature, also incorporates two parts, one dealing with vehicle–track-viaduct dynamics and the other dealing with sound radiation from the girders, but takes into account more features related to high-speed. In this model, vehicle–track-viaduct dynamics is dealt with in the frequency-domain based on the theory of infinitely long periodic structure and the Fourier-series method, predicting vibration frequency spectra for each and every box girder. The predicted vibration frequency spectra of all the box girders are expressed as a sum of propagating waves at different wavenumbers, and sound radiation from each propagating wave is evaluated using the 2.5D acoustic boundary element method. This approach to sound radiation enables contributions from all the box girders to be included at a reasonable computational cost. This paper continues with a comparison in bridge vibration and noise between prediction and measurement for a typical site. And finally, based on the parameters of that site, characteristics of noise radiation from the concrete box girders are studied using the prediction model.