Resonance ultrasound spectroscopy (RUS) is a nondestructive technique for evaluating elastic and an-elastic material properties. The frequencies of free vibrations for a carefully crafted sample are measured, and material properties can be extracted from this. In one popular application, the determination of monocrystal elasticity, the results are not always reliable. In some cases, the resonant frequencies are insensitive to changes in certain elastic constants or their linear combinations. Previous work has been done to characterize these sensitivity issues in materials with isotropic and cubic symmetry. This work examines the sensitivity of elastic constant measurements by the RUS method for materials with hexagonal symmetry, such as titanium-diboride. We investigate the reliability of RUS data and explore supplemental measurements, namely, surface acoustic wave (SAW) to obtain an accurate and complete set of elastic constants.

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.

A characteristic feature of nonlinear vibrations is the energy transfer among different parts or modes of a mechanical system. Moreover, nonlinear vibrations are often non-periodic, even at steady state. To analyze these phenomena experimentally, the vibration response must be measured at multiple locations in a time-synchronous way. For this task, piezoelectric accelerometers are by far the most popular technology. While the effect of attached sensors on linear vibration properties is well-known (mass loading in particular), the purpose of the present work is to assess their intrusiveness on nonlinear vibrations. To this end, we consider a compressor blade that undergoes impacts near the tip for sufficiently large vibrations. We consider two configurations, one in which five triaxial piezoelectric accelerometers are glued to the blade surface and one without sensors attached. In both configurations, the vibration response is measured using a multi-point laser Doppler vibrometer. In the linear case without impacts, the lowest-frequency bending mode merely sees the expected slight frequency shift due to mass loading. In the nonlinear vibro-impact case, unexpectedly, the near-resonant response to harmonic base excitation changes severely both quantitatively and qualitatively. In particular, pronounced strongly modulated responses and period doubling are observed only in the case without attached sensors. We conjecture that this is due to a considerable increase of damping, caused by the sensor cables, affecting mainly the higher-frequency modes.

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 work, the reverse dispersion entropy (RDE) is used to process the squared envelope (SE) signal in order to detect nonstationarites. Based on the idea of spectral kurtosis (SK) and kurtogram, the squared envelope signal is first extracted by applying the short time Fourier transform to vibration signal. Then, as an alternative to negative Shannon entropy, the RDE is used to process the squared envelope to detect the range of frequencies at which the transients occur. The RDEgram color-coded map is used to represent the RDE values as a function of frequency and frequency resolution from which the ideal filter parameters can be inferred. Once the best frequency and frequency bandwidth pair are found, an optimum finite impulse response filter can be designed to filter the original vibration signal. The proposed method is tested against simulated and actual vibration signals and proved to be superior to existing methods.

This study presents new straightforward benchmark solutions for bending and free vibration of clamped anisotropic rectangular thin plates by a double finite integral transform method. Being different from the previous studies that took pure trigonometric functions as the integral kernels, the exponential functions are adopted, and the unknowns to be determined are constituted after the integral transform, which overcomes the difficulty in solving the governing higher-order partial differential equations with odd derivatives with respect to both the in-plane coordinate variables, thus goes beyond the limit of conventional finite integral transforms that are only applicable to isotropic or orthotropic plates. The present study provides an easy-to-implement approach for similar complex problems, extending the scope of finite integral transforms with applications to plate problems. The validity of the method and accuracy of the new solutions that can serve as benchmarks are well confirmed by satisfactory comparison with the numerical solutions.

Low-frequency sound attenuation is often pursued using Helmholtz resonators (HRs). The introduction of a compliant wall around the acoustic cavity results in a two degrees-of-freedom (2DOF) system capable of more broadband sound absorption. In this study, we report the amplitude-dependent dynamic response of a compliant-walled HR and investigate the effectiveness of wall compliance to improve the absorption of sound in linear and nonlinear regimes. The acoustic-structure interactions between the conventional HR and the compliant wall result in non-intuitive responses when acted on by nonlinear amplitudes of excitation pressure. This paper formulates and studies a reduced order model to characterize the nonlinear dynamic response of the 2DOF HR with a compliant wall compared to that of a conventional rigid HR. Validated by experimental evidence, the modeling framework facilitates an investigation of strategies to achieve broadband sound attenuation, including by selection of wall material, wall thickness, geometry of the HR, and other parameters readily tuned by system design. The results open up new avenues for the development of efficient acoustic resonators exploiting the deflection of a compliant wall for suppression of extreme noise amplitudes.

Fractal lattice is a kind of lattices with multifunctional physical characteristics and superior mechanical properties. The wave propagation of the triangular lattice with Koch fractal is calculated by the finite element method and Bloch theorem. The effects of the iteration number on the band gaps and the band edge modes are studied. The finite element software was used to simulate the dynamic response of the triangular lattice with Koch fractal for verifying the vibration suppression performance. The results show that the triangular lattice with Koch fractal can produce multiple and low-frequency band gaps. As an increase of the iteration number, the band gap gradually shifts to a lower frequency. By comparing and analyzing the band edge modes and the eigenmodes of Koch fractal, the mechanisms of the band gaps within the low-frequency ranges are analyzed and discussed in detail. Additionally, the band edge modes exhibit similar vibration modes. Finally, the simulation results of the finite lattice verify the broadband vibration suppression performance of the triangular lattice with Koch fractal. This work provides insights into the lattice dynamic behavior adjusted by Koch fractal, which is beneficial to the periodic lattice for suppressing vibration in engineering applications.

Locally resonant materials allow for wave propagation control in the subwavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this article, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e., its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.

In this work, the elastic wave propagation and dispersion characteristics of a curved tapered frame structure are investigated analytically. Separately, wave propagation through uniform curved and straight tapered beam was reported in the existing literature; however, no literature reports the influence of simultaneous bent and taper on the wave propagation. In particular, the band characteristics for the curved and tapered beam with two types of cross sections, i.e., rectangular and circular, are presented. The paper elucidates that introducing a small periodic bent angle cross section produces a complete, viz., axial and flexural bandgap in the low-frequency region, and conicity enhances the width of the band. It is also evidenced that a curved tapered frame with a solid circular cross section induces a wider bandgap than the rectangular section. A complete first normalized bandwidth of 159% is achievable for the circular cross section and 123% in the case of the rectangular section. The complete result is presented in a non-dimensional framework for wider applicability. An analysis of a finite tapered curved frame structure also demonstrates the attenuating characteristics obtained from the band structure of the infinite structure. The partial wave mode conversion, i.e., generation of coupled axial and flexural mode from a purely axial or flexural mode in an uncoupled medium, is observed. This wave conversion is perceived in reflected and transmitted waves while this curved tapered frame is inserted between the two uniform cross-sectional straight frames.

Signal denoising has been significantly explored in various engineering disciplines. In particular, structural health monitoring applications generally aim to detect weak anomaly responses (including acoustic emission (AE)) generated by incipient damage, which are easily buried in noise. Among various approaches, stochastic resonance (SR) has been widely adopted for weak signal detection. While many advancements have been focused on identifying useful information from the frequency domain by optimizing parameters in a post-processing environment to activate SR, it often requires detailed information about the original signal a priori, which is hardly assessed from signals overwhelmed by noise. This research presents a novel online signal denoising strategy by utilizing SR in a parallel array of bistable systems. The original noisy input with additionally applied noise is adaptively scaled, so that the total noise level matches the optimal level that is analytically predicted from a generalized model to robustly enhance signal denoising performance for a wide range of input amplitudes that are often not known in advance. Thus, without sophisticated post-processing procedures, the scaling factor is straightforwardly determined by the analytically estimated optimal noise level and the ambient noise level, which is one of the few quantities that can be reliably assessed from noisy signals in practice. Along with numerical investigations that demonstrate the operational principle and the effectiveness of the proposed strategy, experimental validation of denoising AE signals by employing a bistable Duffing circuit system exemplifies the promising potential of implementing the new approach for enhancing online signal denoising in practice.

In this paper, a simple and efficient method is developed to quench the steady-state vibration of a harmonically excited, damped and symmetric laminated composite rectangular plate. This is achieved by enforcing points of zero displacement, or nodes, at some specified locations on the laminated composite plate using properly tuned damped oscillators. Using the assumed-modes method, the governing equations of the laminated composite plate carrying the damped oscillators are first formulated. A set of constraint equations is established by enforcing nodes at user-specified locations on the plate. Two attachment scenarios are considered: when the attachment and node locations coincide and when they are distinct. Numerical experiments show that for both cases, the damped oscillator parameters can be readily determined and the desired node locations can be successfully imposed. More importantly, enforcing nodes can suppress vibration in the vicinity of the node locations, thereby keeping that region of the laminated composite plate nearly stationary.

Planetary gearboxes are susceptible to premature failures due to cyclic random loadings and extreme operating conditions. Fault diagnostics strategies are crucial to increase operational safety and reduce economic costs. This led to the research question is: Can a deep convolutional neural network (DCNN) with data fusion improve diagnostics of a planetary gearbox using simulated data? To answer this question, a DCNN framework was proposed to diagnose planetary gearbox with crack using simulated time and the frequency response. A finite element model was developed to generate a time-varying mesh stiffness response for gear tooth meshing at different crack levels. The mesh stiffness was expanded in terms of the Fourier series to generate values at any rotational speed and time interval. The generated mesh stiffness response was used on a dynamic model to generate the time and frequency response of the system. An additional data set was generated using feature-level data fusion. The two datasets were fed to the DCNN model to diagnose the crack faults and results were compared. It was shown that the feature-level data fusion method is very robust in diagnosing crack faults with good accuracy rates even with the presence of a high level of noise.

A local-domain wave packet enriched multiphysics finite element (FE) formulation is employed for accurately solving axisymmetric wave propagation problems in elastic and piezoelastic media, involving complex wave modes and sharp jumps at the wavefronts, which pose challenges to the conventional FE solutions. The conventional Lagrangian interpolations for the displacement and electric potential fields are enriched with the element-domain sinusoidal functions that satisfy the partition of unity condition. The extended Hamilton’s principle is employed to derive the coupled system of equations of motion which is solved using the simple Newmark- β direct time integration scheme without resorting to any remeshing near the wavefronts or post-processing. The performance of the enrichment is assessed for the axisymmetric problems of impact waves in elastic and piezoelectric cylinders and elastic half-space, bulk and Rayleigh waves in the semi-infinite elastic domain and ultrasonic Lamb wave actuation and propagation in plate-piezoelectric transducer system. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for all problems, including those involving multiple complex wave modes and sharp discontinuities in the fields at the wavefronts.

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.

Strongly nonlinear structures have attracted a great deal of attention in energy harvesting and vibration isolation recently. However, it is challenging to accurately characterize the nonlinear restoring force using analytical modeling or cyclic loading tests in many realistic conditions due to the uncertainty of installation parameters or other constraints, including space size and dynamic disturbance. Therefore, a displacement-measurement restoring force surface identification approach is presented for obtaining the nonlinear restoring force. Widely known quasi-zero stiffness, bistable, and tristable structures are designed in a cantilever-beam system with coupled rotatable magnets to illustrate the strongly nonlinear properties in the application of energy harvesting and vibration isolation. Based on the derived physical model of the designed strongly nonlinear structures, the displacement-measurement restoring force surface identification with a least-squares parameter fitting is proposed to obtain the parameters of the nonlinear restoring force. The comparison between the acceleration integration and displacement differentiation methods for describing the restoring force surface of strongly nonlinear structures is discussed. Besides, the influence of the noise level on identification accuracy is investigated. In experimental conditions, quasi-zero stiffness, bistable, and tristable nonlinear structures with various geometrical parameters are utilized to analyze the identified nonlinear restoring force curve and measured force–displacement trajectory. Finally, experimental results verify the effectiveness of the displacement–measurement restoring force surface method to obtain the nonlinear restoring force.

Vibration energy harvesting problems have strongly developed in recent years. However, many researchers just consider bending vibration models of energy harvesters. As a matter of fact, torsional vibration is also important and cannot be ignored in many cases. In this work, closed-form solutions of bending-torsion coupled forced vibrations of a piezoelectric energy harvester subjected to a fluid vortex are derived. Timoshenko beam model is used for modeling the energy harvester, and the extended Hamilton’s principle is used in the modeling process. Since piezoelectric effects in both bending and torsional directions are considered, two kinds of electric coupling effects appear in forced vibration equations, and a new model for the electric circuit equation is developed. Lamb–Oseen vortex model is considered in this study. Both the external aerodynamic force and moment are simple harmonic loads. Three damping coefficients are considered in the present model. Based on Green’s function method, closed-form solutions of the piezoelectric energy harvester subjected to the fluid vortex are derived. Some published results are used to verify the present solutions. It can be concluded through analysis that when torsional vibration is considered, the bandwidth of the high energy area of the voltage becomes large and the bending-torsion coupled vibration energy harvester can produce more power than a transverse vibration energy harvester.

This paper focuses on the radiation modes and efficiency of propeller tonal noise. The thickness noise and loading noise model of propellers has been formulated in spherical coordinates, thereby simplifying numerical evaluation of the integral noise source. More importantly, the radiation field can be decomposed and projected to spherical harmonics, which can separate source-observer positions and enable an analysis of sound field structures. Due to the parity of spherical harmonics, the proposed model can mathematically explain the fact that thrusts only produce antisymmetric sound waves with respect to the rotating plane. In addition, the symmetric components of the noise field can be attributed to the thickness, as well as drags and radial forces acting on the propeller surface. The radiation efficiency of each mode decays rapidly as noise sources approach the rotating center, suggesting the radial distribution of aerodynamic loadings should be carefully designed for low-noise propellers. The noise prediction model has been successfully applied to a drone propeller and achieved a reliable agreement with experimental measurements. The flow variables employed as an input of the noise computation were obtained with computational fluid dynamics (CFD), and the experimental data were measured in an anechoic chamber.

Aiming at reducing the high-amplitude and wide-frequency noise in charged air intake system of the powertrain, this paper proposes a new method for predicting the acoustic characteristics of an irregular cross-section multi-chamber perforated resonator under flow conditions. By this method, the presence of three-dimensional sound waves and the effects of higher-order modes are considered, and the acoustic performance of the resonator can be evaluated through the computation of transmission loss. Moreover, by discretizing the cross-section of the perforated resonator and extracting node information, this method can solve the acoustic characteristics of the perforated resonator with any cross section. Based on the transfer matrix method, the quadrupole parameters of each chamber are obtained. Then, the acoustic characteristics of the multi-chamber perforated resonator could be calculated. The theoretical prediction data and the experimental data have been compared, and the results show good agreement within the entire frequency range, which verifies the accuracy of the theoretical prediction approach. Based on this prediction approach, the influence of section ratio, structure parameters, and inlet flowrate on the acoustic characteristics of the resonator is explored. The results show that when the structural parameters change, the peak resonance frequency of the resonator will have a regular shift. With the increase of the inlet flowrate, the main frequency band of sound attenuation will decrease significantly. The theoretical method developed in this work can be used for the calculation and optimization of multi-chamber resonators in various applications.

This paper investigates the shock isolation characteristics of an electromagnetic bistable vibration isolator (BVI) with tunable magnetic controlled stiffness. The theoretical model of the BVI is established. The maximum acceleration ratio (MAR), maximum absolute displacement ratio (MADR), and maximum relative displacement ratio (MRDR) are introduced to evaluate the shock isolation performance of the BVI. The kinetic and potential energy are observed to further explore the performance of the BVI. The effects of the potential barrier, shape of potential well, and damping ratio on the BVI are discussed compared with the linear vibration isolators (LVIs). The results demonstrate that the intrawell oscillations and snap-through oscillations are determined by the excitation amplitude and duration time of main pulse. MADR and MRDR of the BVI are smaller than those of the LVI. The maximum acceleration peak amplitude of the BVI is far below that of the LVI, especially when the snap-through oscillation occurs. In brief, the proposed BVI has a better shock isolation performance than the LVI and has the potential to suppress the shock of space structures during the launch and on-orbit deploying process.