Showing papers in "Journal of Vibration and Acoustics in 2022"

Energy Transfer of an Axially Loaded Beam with a Parallel-Coupled Nonlinear Vibration Isolator

Abstract: Traditional vibration isolation of satellite instruments has an inherent limitation—that low-frequency vibration suppression leads to structural instability. This paper explores a parallel-coupled quasi-zero stiffness (QZS) vibration isolator for an axially loaded beam, with the goal of enhancing the effectiveness of low-frequency isolation. A QZS contains two magnetic rings, which contribute negative stiffness, and one spiral spring, with positive stiffness, a combination that has high static stiffness to resolve the structural instability. The frequency response functions (FRFs) of power flow are used to measure the effectiveness of vibration isolation. The magnetic stiffness of the magnetic rings is calculated using the principle of equivalent magnetic charge. The heights, radii, and gap of the magnetic rings affect its stiffness. The parallel-coupled QZS vibration isolator of an axially loaded beam is modeled using an energy method. Based on the Galerkin truncation, harmonic balance analysis, and arc-length continuation, an approach is proposed to analyze the FRFs of power flow for the parallel-coupled QZS vibration isolation of an axially loaded beam. Numerical results support the analytical results. Both analytical and numerical results show that the power reduction of axially loaded beams with a parallel-coupled quasi-zero vibration isolation system is more significantly suppressed at low frequencies.

Wave propagation in Timoshenko-Ehrenfest nanobeam: A mixture unified gradient theory

Abstract: A size-dependent elasticity theory, founded on variationally consistent formulations, is developed to analyze the wave propagation in nano-sized beams. The mixture unified gradient theory of elasticity, integrating the stress gradient theory, the strain gradient model, and the traditional elasticity theory, is invoked to realize the size-effects at the ultra-small scale. Compatible with the kinematics of the Timoshenko–Ehrenfest beam, a stationary variational framework is established. The boundary-value problem of dynamic equilibrium along with the constitutive model is appropriately integrated into a single functional. Various generalized elasticity theories of gradient type are restored as particular cases of the developed mixture unified gradient theory. The flexural wave propagation is formulated within the context of the introduced size-dependent elasticity theory and the propagation characteristics of flexural waves are analytically addressed. The phase velocity of propagating waves in CNTs is inversely reconstructed and compared with the numerical simulation results. A viable approach to inversely determine the characteristic length-scale parameters associated with the generalized continuum theory is proposed. A comprehensive numerical study is performed to demonstrate the wave dispersion features in a Timoshenko–Ehrenfest nanobeam. Based on the presented wave propagation response and ensuing numerical illustrations, original benchmark for numerical analysis is detected.

Experimental and Theoretical Investigation of Vibro-impact Motions of a Gear Pair Subjected to Torque Fluctuations to Define a Rattle Noise Severity Index

Abstract: Abstract Vibro-impacts are common in various automotive engine and transmission gear applications. They are known to cause excessive noise levels, often called rattling or hammering. Input and output fluctuations acting on such systems cause tooth separations and sequences of impacts allowed by backlash at the gear mesh interfaces. The fluctuations leading gear rattling have often been studied for specific applications with the excitations produced typically by an internal combustion engine. As such, rattle evaluations have been often empirical and specific to the systems considered. In this study, an experimental test setup of a gear pair is developed to emulate the same torque fluctuations in a laboratory environment. This setup is used to establish an impact velocity-based rattle severity index defined by the measured torsional behavior of the drive train that is shown to correlate well with the measured sound pressure levels. With that, a validated dynamic model of the experimental setup is employed to predict the same index to allow estimation of rattle noise outcome solely from a torsional dynamic model of the drivetrain. Predicted rattle severity indexes are shown to agree well with the measured ones within wide ranges of torque fluctuations and backlash magnitudes, allowing an assessment of rattle performance of a drivetrain solely from a torsional model.

Operational Modal Analysis of a Rotating Structure Subject to Random Excitation Using a Tracking Continuously Scanning Laser Doppler Vibrometer via an Improved Demodulation Method

Abstract: A new operational modal analysis (OMA) method is developed for estimation of modal parameters (MPs) of a rotating structure (RS) subject to random excitation using a nonuniform rotating beam model, an image processing method, and an improved demodulation method. The solution to the governing equation of a nonuniform rotating beam is derived, which can be considered as the response of the beam measured by a continuously scanning laser Doppler vibrometer (CSLDV) system. A recently developed tracking CSLDV system can track and scan the RS. The image processing method determines the angular position of the RS so that the tracking CSLDV system can sweep its laser spot along a time-varying path on it. The improved demodulation method obtains undamped mode shapes (UMSs) of the RS by multiplying its measured response by sinusoids whose frequencies are its damped natural frequencies (DNFs) that are obtained from the fast Fourier transform (FFT) of the measured response. Experimental investigation of the OMA method using the tracking CSLDV system is conducted, and MPs of a rotating fan blade (RFB), including DNFs and UMSs, with different constant speeds and its instantaneous MPs with a nonconstant speed are estimated. Estimated first DNFs and UMSs of the stationary fan blade and RFB are compared with those from the lifting method that was previously developed by the authors.

Low-Frequency Multimode Vibration Suppression of an Acoustic Black Hole Beam by Shunt Damping

Abstract: Abstract The ideal acoustic black hole (ABH) can achieve wave gathering and zero reflection of elastic waves. In practice, ABHs have to be truncated, limiting their application in lower frequency range. Aiming at improving the ABH beam's vibration suppression ability at low frequencies, this study proposes a shunt damping-ABH composite beam by pasting shunt damping instead of ordinary damping on the ABH tip. The energy method is employed to solve the vibration equation of the ABH beam. The admissible function is the Mexican hat wavelet. The proposed method is verified by the finite element method. Compared with the uniform beam, the numerical results show the ABH beam has a noticeable attenuating effect in high-frequency range due to the ABH effect, but almost has no attenuating effect in the low-frequency range. Therefore, we introduce shunt damping to enhance the low-frequency vibration control. The shunt damping is composed of circuits connected to a piezoelectric patch. The effects of different circuits connected to the piezoelectric patch are discussed. The R–L shunt circuit and L–C parallel blocking circuit can simultaneously suppress the multimode vibration peak of the ABH beam at the low frequency successfully. Finally, a vibration experiment of ABH beam combined with shunt damping is implemented to verify the present method's feasibility and the shunt damping effect. The proposed shunt damping-ABH composite beam could improve the suppressing ability in both the low and high-frequency ranges.

A Circular Eccentric Vibration Absorber with Circumferentially Graded Acoustic Black Hole Features

Abstract: 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.

Basic Constraints for Design Optimization of Cubic and Bistable Nonlinear Energy Sink

Abstract: This work mainly concentrates on the optimization of cubic and bistable NES to find the maximum efficiency point under harmonic excitation. The conservative system is considered to reveal the inner property of the damping system. With the application of the multiple scales method and the complex variables method, the threshold of excitation and different response regimes are distinguished under the assumption of 1:1 resonance. The maximum efficiency point of cubic and bistable NES occurs when SMR disappears. The factors that affect the optimal efficiency limit are explored. The result indicates that the maximum absorption efficiency level is mainly determined by the damping parameters. Compared with the cubic case, the bistable case involves more complex regimes in terms of chaos oscillation. The influence of damping parameters on the chaos threshold is discussed to adopt different energy levels. With the help of analytical predictions, the proper nonlinear stiffness is determined for certain harmonic excitation. This work offers some fundamental insights into the optimal design of cubic and bistable NES.

Finite Cross-Section Method (FCSM) for Mode Shape Recognition of Highly Coupled Beam-Type Structures

Abstract: The mode shapes of beam-type structures, such as aircraft wings and wind turbine blades, involve a high degree of coupling between bending and torsional deformation. In the case of wind turbine blades, different types of deformation are typically easily recognized by visual observation. However, this visual approach is sometimes challenging for high-order mode shapes, which involve coupling of both bending and torsional deformations. This work proposes a novel mode shape recognition algorithm, called Finite Cross-Section Method (FCSM), for application to highly coupled beam-type structures not only to identify the deformation components of the complex beam mode shapes, but more importantly, to quantify their respective relative contribution. In the application case study for the FCSM method, the entire structure is discretized into multiple cross-sections. The flap-wise, edge-wise, and torsional deformation components of the entire structure are determined at the cross-section level. The deformation components of the entire structure and their respective contribution is obtained from assembling all cross-sections. To validate the mode shape recognition performance, FCSM is applied to and demonstrated on four test cases: (1) numerical mode shapes of a simple cantilever beam, (2) numerical mode shapes from a straight wind turbine blade, (3) numerical mode shapes of a swept wind turbine blade, and (4) experimental mode shapes from a high spatial resolution 3D SLDV modal test. Both numerical and experimental studies demonstrate that FCSM can successfully recognize the quantitative contribution of flap-wise, edge-wise, and torsional deformation.

Acoustic performance of a metascreen-based coating for maritime applications

Abstract: Time and frequency domain numerical models are developed to investigate the acoustic performance of metasurface coatings for marine applications. The coating designs are composed of periodic air-filled cavities embedded in a soft elastic medium, which is attached to a hard backing and submerged in water. Numerical results for a metamaterial coating with cylindrical cavities are favourably compared with analytical and experimental results from the literature. Frequencies associated with peak sound absorption as a function of the geometric parameters of the cavities and material properties of the host medium are predicted. Variation in the cavity dimensions that modifies the cylindrical-shaped cavities to flat disks or thin needles is modelled. Results reveal that high sound absorption occurs when either the diameter or length of the cavities is reduced. Physical mechanisms governing sound absorption for the various cavity designs are described.

Primary parametric amplification in a weakly forced Mathieu equation

Abstract: The present study deals with the response of a forced Mathieu equation with damping, with weak harmonic direct excitation at the same frequency as the parametric excitation. A second-order perturbation analysis using the method of multiple scales unfolds parametric amplification at primary resonance. The parametric effect on the primary resonance behavior occurs with a slow time scale of second order, although the effect on the steady-state response is of order one. As the parametric excitation level increases, the response at primary resonance stretches before becoming unbounded and unstable. Analytical expressions for predicting the response amplitudes are presented and compared with numerical results for a specific set of system parameters. Dependence of the amplification behavior, and indeed possible deamplification, on parameters is examined. The effect of parametric excitation on the response phase behavior is also presented.

Flexural wave propagation in rigid elastic combined metabeam

Abstract: In this paper, flexural wave propagation, attenuation and reflection through finite number of rigid elastic combined meta-beam (RECM) elements sandwiched between two Euler Bernoulli beams has been studied, implementing the spectral element, inverse Fourier transform and transfer matrix method. Spectral element has been formulated for the unit representative cell of RECM employing the rigid-body dynamics. Governing dimensionless parameters are identified. Further, the sensitivity analysis has been carried out to comprehend the influence of non-dimensional parameters such as mass ratio, length ratio, and rotary inertia ratio on the attenuation profile. Rotary inertia of rigid body produces Local resonance(LR) band, which may abridge the gap between the two Bragg Scattering(BS) bands and results in an ultra-wide stop-band for the specific combination of governing non-dimensional parameters. 164% normalized attenuation band is possible to obtain in RECM. Natural frequencies for the finite RECM have also been evaluated from the global spectral element matrix and observed that some natural frequencies lies in the attenuation band. Therefore, the level of attenuation near that natural frequencies is significantly less and cannot be identified from the dispersion diagram of the infinite RECM.

A Robust Delayed Resonator Construction using Amplifying Mechanism

Abstract: The delayed resonator (DR) is an active vibration absorber, which yields ideal vibration suppression at its resonance frequency. In this study, we further complement the DR design in a distinctive mechanical path by introducing an amplifying mechanism (AM), so the creation of DRA. Very different from the existing works that focus more on how to enhance the ideal vibration suppression of the DR, we are interested in how the DR behaves under uncertainties and how can the newly proposed DRA abate the arising negative effects. First, we study the effects of such uncertainties in detecting the excitation frequency on the quality of vibration suppression, working space of the absorber, and energy cost. Then, we discuss how the control parameter perturbation affects the system stability. A comparative study between the classic DR and the proposed DRA is presented throughout the text, showing that the enhanced performance and robustness characteristics enabled by the AM are almost all-around while posing no additional controller complexity. We also show using spectral analysis that the AM can also enhance the transient behavior of the system. Finally, three numerical simulations included as core studies vividly exhibit DRA’s practical strength.

Transient Vibroacoustic Analysis of Functionally Graded Plates

Abstract: This paper presents the vibroacoustic response of pure functionally graded (FG) plates under transient loading of mechanical nature. The functionally graded plate is modeled using the conventional first-order shear deformation theory (FSDT) 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.

Topology Optimization and Wave Propagation of Three-dimensional Phononic Crystals

Abstract: Phononic crystals are periodically engineered structures with special acoustic properties that natural materials cannot have. One typical feature of phononic crystals is the emergence of band gaps wherein the wave propagation is prohibited due to the spatial periodicity of constituents. This paper presents a generalized plane wave expansion method (GPWEM) and a voxel-based discretization technique to calculate the band structures of given three-dimensional phononic crystals. Integrated with the adaptive genetic algorithm (AGA), the proposed method is used to perform topological optimization of constituent distribution to achieve maximized band gap width. Numerical results yielded from the optimization of a three-dimensional cubic phononic crystal verify the effectiveness of the proposed method. Eigenmodes of the phononic crystal with the optimized topology are investigated for a better understanding of the mechanism of band gap broadening.

Satellite vibration isolation using periodic acoustic black hole structures with ultrawide bandgap

Abstract: A lightweight whole-spacecraft vibration isolation system with broadband vibration attenuation capability is of great significance to the protection of satellites during the launch phase. The emergence of metamaterials / phononic crystals provides new ideas for the design of such isolation systems. This letter reports a new type of satellite isolation system to isolate shock and vibrations in an ultrawide frequency range. The labyrinth design of this system integrates acoustic black holes (ABHs) as microstructures, which leads to a significant impedance mismatch and enhances the bandgap effect. The ultrawide vibration and shock attenuation ability of the proposed design is confirmed through band structure and transmission analyses as well as the hammer and falling tests, showing the potential for vast isolation applications.

Active Vibration Control on a Smart Composite Structure Using Modal-Shaped Sliding Mode Control

Abstract: Abstract This article proposes an active modal vibration control method based on a modal sliding mode controller applied to a smart material composite structure with integrated piezoelectric transducers as actuators and sensors. First, the electromechanical coupled system is identified using a modal reduced-order model. The sliding surface is based on the modal-filtered states and designed using a general formulation allowing the control of multiple vibration modes with multiple piezoelectric sensors and actuators. The performance and stability of the nonlinear controller are addressed and confirmed with the experimental results on a composite smart spoiler-shaped structure. The nonlinear switching control signal based on the modal-shaped sliding surface improves performances of the linear part of the control while maintaining not only stability but also robustness. The attenuation level achieved on the target modes on all piezoelectric sensors starts from −14 dB up to −22 dB, illustrating the strong potential of nonlinear switching control methods in active vibration control.

Damping and Bandgap Characteristics of a Viscoelastic Tensegrity Damper

Abstract: A theoretical and experimental investigation of a new class of a tensegrity-based structural damper is presented. The damper is not only capable of attenuating undesirable structural vibrations, as all conventional dampers, but also capable of completely blocking the transmission of vibration over specific frequency bands by virtue of its periodicity. Such dual functionality distinguishes the tensegrity damper over its counterparts of existing structural dampers. Particular emphasis is placed here in presenting the concept and developing the mathematical model of the dynamics of a unit cell the damper. The model is then coupled with a Floquet–Bloch analysis in order to identify the bandgap characteristics of the damper. The predictions of the mathematical model are validated experimentally using a prototype of the damper which is built using 3D printing. Comprehensive material characterization of the damper is performed followed by a detailed extraction of the static and dynamic behavior of the damper in order to validate the theoretical predictions. Close agreement is observed between theory and experiments. The developed theoretical and experimental techniques provide invaluable means for the design of this new class of dampers, particularly for critical structural applications.

Vibratory Conveying by Harmonic Longitudinal and Polyharmonic Normal Vibrations of Inclined Conveying Track

Abstract: Vibratory conveying of a material point by harmonic longitudinal and polyharmonic normal vibrations of an inclined conveying surface is considered. The dependence of dimensionless conveying velocity – a ratio of velocity to the product of frequency and amplitude of longitudinal vibration – on several dimensionless parameters is investigated in the moving modes without hopping. Maximal conveying velocity is achieved at the certain values of normal vibration amplitudes and phase difference angle between the longitudinal and normal vibrations, which are called optimal. Their values are dependent on two dimensionless parameters: the inclination angle parameter – a ratio of an inclination angle tangent to a frictional coefficient, the intensive vibration coefficient – a ratio of the longitudinal amplitude of vibration to the amplitude of the first harmonic of normal vibration and frictional coefficient. In a condition of the intensive longitudinal vibration, when its amplitude significantly greater than amplitudes of normal vibration, dimensionless velocity is almost independent of the intensive vibration parameter and it depends only on inclination angle parameter, i.e. on inclination angle and frictional coefficient. The optimal values of harmonics' amplitudes of polyharmonic normal vibration are determined in dependence of inclination angle parameter with the number of harmonics from 2 to 7. The graphs of considered dependencies are presented and the most important values of parameters are presented in the table. Conclusions are made to determine the optimal vibration parameters and the problems of further research are indicated. The considered vibrations can be used in different vibratory conveying devices with electromagnetic drives.

A simple configuration of an actively synthesized gyroscopic-nonreciprocal acoustic metamaterial

Abstract: A simple configuration of an active Nonreciprocal Gyroscopic Meta-Material (NGMM) is presented. In the proposed NGMM system, a one-dimensional acoustic cavity is provided with piezoelectric boundaries acting as a collocated pair of sensors and actuators. The active piezo-boundaries are controlled by a simple control algorithm that synthesizes a virtual gyroscopic control action to impart desirable non-reciprocal characteristics which are tunable both in magnitude and phase. The dynamic model of a prototype of the NGMM cell is experimentally identified in an attempt to provide means for predicting the characteristics of the virtual gyroscopic controller for various control gains during forward and backward propagations. The theoretical predictions are validated experimentally without the need for any physical dynamic controller which was provided, in previous studies, by using a dummy NGMM cell. Such a simplified arrangement enables the fast execution of the controller with enhanced frequency bandwidth capabilities. The experimental and theoretical characteristics of the NGMM cell are monitored and predicted for different control gain in order to evaluate its behavior for both forward and backward propagation. The obtained experimental results are compared with the theoretical predictions and are found to be in close agreement. The presented concepts provide the foundation necessary for implementation of NGMM that can be employed to more complex 2D and 3D critical structures in order to achieve non-reciprocal behavior in a simple and programmable manner.

Resonance Risk and Mode Shape Management in the Frequency Domain to Prevent Squeak and Rattle

Abstract: Avoiding quality problems in passenger cars, such as squeak and rattle (S&R), has been a remarkable cost-saving consideration. The introduction of electric engines and autonomous driving is expected to further stress the need for quieter cabins. However, the complexity of S&R events has obstructed the practical treatment of these quality issues in the pre-design-freeze phases of product development. In this study, new quantified frequency-domain metrics are proposed to measure the risk of S&R generation in car subsystems. The proposed metrics measure the resonance risk and the mode shape similarity in the critical interfaces for S&R. The calculations are done based on the system response in the frequency domain. Compared with the time-domain evaluation methods, the knowledge about the system excitation levels is not essential and the calculations are more time-efficient. The proposed metrics can be used in design optimization processes to involve S&R attributes in the pre-design-freeze attribute trade-off activities besides other attributes. In this work, these metrics were used in a previously developed two-stage optimization approach to determine the connection configuration in two industrial cases. As compared with the baseline design, the risk for S&R was reduced by improving the system behavior in terms of resonance risk and mode shape similarity. This was achieved by applying adjustments to the location of the fasteners while maintaining the same general connection configuration concept.

Estimation of energy pumping time in bistable NES and experimental validation

Abstract: The bistable Nonlinear Energy Sink (NES) shows high efficiency in mitigating vibration through Targeted Energy Transfer (TET). It performs well in low and high energy input cases, whereas, for a cubic NES, TET occurs only above a certain energy threshold. In this work, the measure of energy pumping time is extended to a harmonic excitation case by the application of a particular integration assumption. An equivalent point in the SIM structure can represent the average variation of the amplitudes of LO and NES. The marked robustness of this semi-analytical prediction method under parameter perturbation is investigated numerically here. The influence of parameters on the rate at which the amplitude declines is also investigated for both impulsive and harmonic excitation. The pumping time estimation is validated in a low energy input experimental test.