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Journal of Sound and Vibration
Journal Prestige (SJR): 1.36
Citation Impact (citeScore): 3
Number of Followers: 215  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0022-460X - ISSN (Online) 1095-8568
Published by Elsevier Homepage  [3182 journals]
  • Special Issue on Vibro-impact and friction dynamics
    • Abstract: Publication date: Available online 11 November 2019Source: Journal of Sound and VibrationAuthor(s): A. Fidlin, V. Silberschmidt
  • Corrigendum to “Higher-order WKB analysis of reflection from tapered
           elastic wedges” [J. Sound Vib. 449 (2019) 368–388]
    • Abstract: Publication date: 17 February 2020Source: Journal of Sound and Vibration, Volume 467Author(s): Angelis Karlos, Stephen J. Elliott, Jordan Cheer
  • Optimized under-actuated control of blade vibration system under wind
    • Abstract: Publication date: Available online 9 November 2019Source: Journal of Sound and VibrationAuthor(s): Nailu Li, Anle Mu, Hua Yang, Kaman T. Magar This paper studies the problem of optimal under-actuated control of blade vibration system (BVS) under wind uncertainty. The nonlinear BVS model is established to reveal limit cycle oscillations in flapwise, edgewise and torsional vibration motions. The difficulty of under-actuated vibration control of BVS lies in manipulating multiple degree of freedom (DOF) motions by single pitch input, and wind uncertainty could further threaten vibration reductions. A novel partial state feedback vibration control scheme is proposed based on modified linear quadratic regulator and linearized BVS. To deal with wind uncertainty, the problem of designing optimal vibration controller is converted into the problem of parameters optimization. A combined correlated differential evolutionary (CC-DE) algorithm is designed to ensure efficient optimization solution. Simulation results show that proposed method has significantly improved vibration reductions in multiple DOF motions, enhanced efficiency in actuator utilization and good performance under diverse wind uncertainties, compared to other conventional methods.
  • Developing a virtual stiffness-damping system for airfoil aeroelasticity
    • Abstract: Publication date: Available online 9 November 2019Source: Journal of Sound and VibrationAuthor(s): Difan Tang, Lei Chen, Zhao Feng Tian, Eric Hu In this research a two-degrees-of-freedom (2-DOF) virtual stiffness-damping system (VSDS) is developed to facilitate industrial and laboratory testing of airfoil aeroelasticity instability. Other existing test-beds in this field rely on elastic elements or structures to set airfoil elasticity in tests, which can be costly and inconvenient in cases of frequent stiffness adjustment across a wide range. A possible alternative is the VSDS that utilizes electric drives to simulate structural elasticity and damping, as seen in marine and bio-mechanical engineering, which however, cannot be directly applied to airfoil aeroelasticity testing (AAT) due to operation requirements and conditions being different. Therefore, in this study a new VSDS is developed specifically for AAT. Firstly, the concept of 1-DOF VSDS is extended to 2 DOFs, with the dynamics coupling between each DOF addressed at the stage of operation principle determination, by the proposed direct force/torque regulation with force/torque feedback. Secondly, resolution loss in position/velocity measurement is identified as a main problem associated with the non-reduction transmission required, and is solved by a modified extended-state observer (MESO) proposed for fast position/velocity estimation. Thirdly, system identification and calibration procedures involved in developing the new VSDS are reduced to minimum through a robust force/torque tracking controller design, with detailed numerical study on parametric analysis given. As validated in wind-tunnel experiments the new VSDS can closely track the desired force/torque and provide satisfactory virtual stiffness and damping in AAT.
  • Nonlinear dynamics of slender inverted flags in uniform steady flows
    • Abstract: Publication date: Available online 8 November 2019Source: Journal of Sound and VibrationAuthor(s): Mohammad Tavallaeinejad, Mathias Legrand, Michael P. Païdoussis A nonlinear fluid-elastic continuum model for the dynamics of a slender cantilevered plate subjected to axial flow directed from the free end to the clamped end, also known as the inverted flag problem, is proposed. The extension of elongated body theory to large-amplitude rotations of the plate mid-plane along with Bollay's nonlinear wing theory is employed in order to express the fluid-related forces acting on the plate, while retaining all time-dependent terms in both modelling and numerical simulations; the unsteady fluid forces due to vortex shedding are not included. Euler-Bernoulli beam theory with exact kinematics and inextensibility is employed to derive the nonlinear partial integro-differential equation governing the dynamics of the plate. Discretization in space is carried out via a conventional Galerkin scheme using the linear mode-shapes of a cantilevered beam in vacuum. The pseudo-arclength continuation technique is adapted to construct bifurcation diagrams in terms of the flow velocity, in order to gain insight into the stability and post-critical behaviour of the system. Integration in time is conducted using Gear's backward differentiation formula. The sensitivity of the nonlinear response of the system to different parameters such as the aspect ratio, mass ratio, initial inclination of the flag, and viscous drag coefficient is investigated through extensive numerical simulations. It is shown that for flags of small aspect ratio the undeflected static equilibrium is stable prior to a subcritical pitchfork bifurcation. For flags of sufficiently large aspect ratio, however, the first instability encountered is a supercritical Hopf bifurcation giving rise to flapping motion around the undeflected static equilibrium; increasing the flow velocity further, the flag then displays flapping motions around deflected static equilibria, which later lead to fully-deflected static states at even higher flow velocities. The results exposed in this study help understand the dynamics of the inverted-flag problem in the limit of inviscid flow theory.
  • Fault diagnosis of planetary gearbox under variable-speed conditions using
           an improved adaptive chirp mode decomposition
    • Abstract: Publication date: Available online 8 November 2019Source: Journal of Sound and VibrationAuthor(s): Shiqian Chen, Minggang Du, Zhike Peng, Zhipeng Feng, Wenming Zhang Fault diagnosis of planetary gearboxes under variable-speed conditions is a challenging task since the vibration signals are non-stationary and have more complicated characteristic components due to the complex gearbox configuration. Effectively identifying and extracting these non-stationary characteristic components are important for fault diagnosis. This paper achieves the goal by exploiting an improved adaptive chirp mode decomposition (I-ACMD) method. The I-ACMD mainly includes two ingredients. Firstly, the algorithm framework of the original ACMD is modified for joint component estimation, which can effectively deal with very close signal components. Secondly, to address the issue of the instantaneous frequency (IF) initialization for I-ACMD, we combine a parameterized demodulation (PD) method with a signal resampling technique to extract multiple IF curves simultaneously. Compared with traditional time-frequency ridge detection methods, the proposed PD-based IF initialization method shows much better interference robustness and thus is more effective to analyze complicated vibration signals of planetary gearboxes. Moreover, with the output results of the I-ACMD, we construct a high-resolution time-frequency representation which can clearly reveal the time-varying gear characteristic frequencies. Both our simulated and experimental studies have shown that the proposed method can effectively indentify very close and weak vibration characteristic components, and thus successfully detect different kinds of gear faults.
  • Measurement of radiated sound power from a complex underwater sound source
           in a non-anechoic pool based on spatial averaging
    • Abstract: Publication date: Available online 8 November 2019Source: Journal of Sound and VibrationAuthor(s): Dajing Shang, Rui Tang, Qi Li, Jiapeng Song The measurement of radiated sound power from a complex underwater sound source in a non-anechoic pool is investigated, taking account of the facts that a non-anechoic pool does not satisfy the conditions for existence of a diffuse field and that the theory applicable to a reverberation room in the air cannot be used for a non-anechoic pool. Based on normal wave theory, a relationship is derived between the spatial average sound pressure level in the reverberation control area far from the source and the sound source radiation power level. The influence on the measurement results of the number of points (i.e., hydrophones) evenly distributed in the non-anechoic pool over which the spatial average is taken is also investigated. The radiated sound power from a marine propulsion system including a propeller is measured using this technique. Both the theoretical and experimental results show that above the cutoff frequency of the non-anechoic pool, the radiated sound power from a complex underwater sound source can be measured accurately using the spatial average method. The radiated sound power from a marine propulsion system including a propeller measured by this method differs from that obtained using the enveloping surface method by no more than 2 dB. The accuracy of the proposed method is related to the number of averaging points evenly distributed in the non-anechoic pool: the greater the number of evenly distributed points, the higher is the accuracy, and the radiated sound power measured using 256 points evenly distributed in the non-anechoic pool differs from the free field result by no more than 2 dB.
  • Sparse time series modeling of the baseline vibration from a gearbox under
           time-varying speed condition
    • Abstract: Publication date: Available online 7 November 2019Source: Journal of Sound and VibrationAuthor(s): Yuejian Chen, Xihui Liang, Ming J. Zuo Time series model-based approach (TSMBA) is promising in processing vibration signals and assessing the health condition of gearboxes. Accurate time series modeling of the baseline vibration is critical to the TSMBA. Gearboxes often operate under time-varying speed condition, which makes the baseline vibration non-stationary. To accurately model such signals, non-stationary time series models are in demand. Conventional functional pooled autoregression (FP-AR) model is a good option. However, conventional FP-AR assumed 1) consecutive AR terms and 2) identical functional space that describes the dependency between AR parameters and rotating speed, which limited its modeling accuracy. To improve modeling accuracy, this paper proposes a sparse FP-AR model that uses sparse AR terms and non-identical functional spaces. To obtain such a sparse FP-AR model, a new model selection procedure is developed by adopting the least absolute shrinkage and selection operator. The sparse FP-AR model has been validated using simulation signals from a simulation model for a fixed-axis gearbox and experimental signals from two independent fixed-axis gearbox test-rigs. The modeling accuracy was measured by mean squared errors and randomness tests of the modeling residuals, goodness-of-fit between the one-step ahead prediction and real gear vibration, and time-frequency spectra. Results have shown that the proposed sparse FP-AR model has higher modeling accuracy than the conventional one. Meanwhile, TSMBA that uses the sparse FP-AR model was applied for detecting gear tooth crack faults under time-varying speed condition. Results have shown that the proposed method benefits the fixed-axis gearbox in early detection of faults and better assessment of fault progressions.
  • Analytical and numerical modelling of non-collinear wave mixing at a
           contact interface
    • Abstract: Publication date: Available online 7 November 2019Source: Journal of Sound and VibrationAuthor(s): L.R. Francis Rose, Philippe Blanloeuil, Martin Veidt, Chun H. Wang An analytical model is presented for wave mixing of two incident non-collinear plane waves at a plane contact interface characterised by a nonlinear traction law that is representative of rough-surface contact, where the normal response is described by a quadratic nonlinearity whereas the tangential response is linear. The approach relies on a decomposition of the scattered field into contributions exhibiting distinctive symmetries with respect to the interface, combined with a perturbation analysis that treats the nonlinear response as a small correction relative to a linear response. The decomposition is shown to lead to uncoupled governing equations, thereby enabling explicit analytical formulae to be derived for the scattered field amplitudes for a linear interface, which in turn provides the source terms for determining the amplitudes and directions of the nonlinear mixed waves. The characteristics of ultrasound wave mixing at an interface are thus shown to differ in several respects from bulk wave mixing due to material nonlinearity. In particular, interface mixing generates mixed waves at the sum and difference frequencies that propagate in both forward and backward directions (transmitted and reflected), whereas bulk mixing only produces a forward propagating mixed wave at the sum frequency. The directions of propagation for interface mixing are determined from the sum or difference of the components of the incident wave vectors parallel to the interface, coupled with the sum or difference of the frequencies, which constitutes a generalisation of Snell's law. These directions generally differ from the sum of the wave vectors that provides the propagation direction for bulk mixing. A computational model is also presented that confirms these predictions of the analytical model. The implications of both models for the design and interpretation of experimental investigations are briefly discussed.
  • A generalized inverse cascade method to identify and optimize vehicle
           interior noise sources
    • Abstract: Publication date: Available online 6 November 2019Source: Journal of Sound and VibrationAuthor(s): H.B. Huang, J.H. Wu, X.R. Huang, M.L. Yang, W.P. Ding The noise, vibration and harshness (NVH) emitted by a vehicle are very important to a customer's perception of the vehicle quality. A vehicle's NVH can be improved by considering the three following facets: the noise source, transfer path, and receiver. The identification and optimization of vehicle interior noise sources is crucial when attempting to reduce noise levels and improve sound quality. Although traditional methods, such as those utilizing sound pressure levels, nearfield acoustic holography, and transfer path analysis, can provide the magnitudes and contributions of noise sources, they cannot present specific methods for optimizing those noise sources. This study proposes a new method, the generalized inverse cascade method (GICM), to solve this problem. The GICM combines systems engineering with the interval optimization technique to identify and optimize vehicle noise sources. Applying the GICM to a decision problem involves the following three steps: (1) constructing the decision problem as a cascade tree; (2) developing a numerical model to quantify the cascade tree; and (3) solving the numerical model using the interval optimization method. A Volkswagen sedan is used in this study as an example, and a vehicular road test and subjective evaluation are implemented to record and evaluate the interior noise. The GICM, identifies potential abnormal interior noise sources, and a modified method is presented to optimize the abnormal noise sources by calculating the feasible intervals of design variables. A verification experiment shows that the vehicle interior noise is successfully optimized, thereby validating the proposed GICM.
  • Explicit third-order model reduction formulas for general nonlinear
           mechanical systems
    • Abstract: Publication date: Available online 6 November 2019Source: Journal of Sound and VibrationAuthor(s): Zsolt Veraszto, Sten Ponsioen, George Haller For general nonlinear mechanical systems, we derive closed-form, reduced-order models up to cubic order based on rigorous invariant manifold results. For conservative systems, the reduction is based on Lyapunov Subcenter Manifold (LSM) theory, whereas for damped-forced systems, we use Spectral Submanifold (SSM) theory. To evaluate our explicit formulas for the reduced model, no coordinate changes are required beyond an initial linear one. The reduced-order models we derive are simple and depend only on physical and modal parameters, allowing us to extract fundamental characteristics, such as backbone curves and forced-response curves, of multi-degree-of-freedom mechanical systems. To numerically verify the accuracy of the reduced models, we test the reduction formulas on several mechanical systems, including a higher-dimensional nonlinear Timoshenko beam.
  • Non-probabilistic method to consider uncertainties in frequency response
           function for vibration-based damage detection using Artificial Neural
    • Abstract: Publication date: Available online 6 November 2019Source: Journal of Sound and VibrationAuthor(s): Khairul H. Padil, Norhisham Bakhary, Muyideen Abdulkareem, Jun Li, Hong Hao Artificial neural network (ANN) has become a popular computational approach in the field of vibration-based damage detection, based on its ability to relate the nonlinear relationship between structural vibration characteristics and damage information. In the meantime, frequency response function (FRF) estimation has been proven effective as a dynamic parameter for damage detection due to its prevention of information leakage. In this regard, FRF is chosen as the input variable for ANN to detect structural damage in this study. However, the main concern in damage detection using FRF with ANN is the size of FRF data. A full-size FRF data will result in a wide composition range of the ANN input layer, thus affecting the iteration divergence in the network training process and resulting in the computational inefficiency. In most applications, principal component analysis (PCA) has been used to reduce the size of the FRF data before being fed to an ANN model. However, as the structures become more complex, the FRF data size also increases. The large size of FRF data may result in the PCA not being effective in selecting important information from the actual FRF data, leading to false damage detection. Moreover, the existence of uncertainties from modelling error and measurement error may also amplify the error in damage detection. Hence, this study proposes a combination of a non-probabilistic method with PCA to consider the problem of the existing uncertainties and the inefficiency of using FRF data in ANN-based damage detection. In this study, ANN is used to relate the FRF data to a damage feature. The input data for the network are the compressed real FRFs and the outputs are the elemental stiffness parameter (ESP). The compressed FRF data obtained from PCA provide a new damage index (DI) that is used as the input layer of the ANN. Based on the interval analysis method, the uncertainties in the new DI are considered to bind together to obtain the interval bound (lower and upper bounds) of the DI changes. The possibility of damage existence (PoDE) is designed to ascertain the relationship between the input and output parameters in the form of undamaged and damaged conditions. The verification conducted on a numerical model and a laboratory tested steel truss bridge model demonstrated that the proposed method is efficient in dealing with uncertainties using FRF for damage detection.
  • Topological edge states in phononic plates with embedded acoustic black
    • Abstract: Publication date: Available online 5 November 2019Source: Journal of Sound and VibrationAuthor(s): Sai Sanjit Ganti, Ting-Wei Liu, Fabio Semperlotti We report on the design of phononic plates based on a periodic lattice of acoustic black holes (ABH) and capable of supporting topological edge states. The design is based on the established concept of the acoustic valley Hall effect (AVHE) that is the elastic analogue of the quantum valley Hall effect (QVHE) for quantum mechanical systems. The basic structure consists of a triangular lattice of circular ABHs whose symmetry guarantees the existence of Dirac dispersion at the corners of the Brillouin zone. Starting from this symmetric lattice, space inversion symmetry (SIS) can be broken by introducing an angle-dependent scaling of the ABH taper profile. Depending on the sign of the scaling factor, two topologically distinct lattice configurations can be obtained and assembled in order to create a domain wall characterized by unconventional dynamic properties. More specifically, such domain wall supports the formation and propagation of quasi-unidirectional elastic guided modes that are topologically protected against back-scattering due to impurities or defects in the lattice.
  • Nonlinear damping in suspended beam micro- and nanoresonators due to
           surface loss
    • Abstract: Publication date: Available online 5 November 2019Source: Journal of Sound and VibrationAuthor(s): André Gusso The nonlinear damping resulting from surface energy loss in suspended beam micro and nanoresonators is investigated theoretically. Surface energy loss is known to be a relevant and in some cases a dominant damping mechanism in micro and nanoresonators. So far, it was only investigated in the linear (low amplitude) regime. In this work we consider the beam as made of an anelastic material and introduce the beam stretching effect in the elastic model of transversally vibrating beams clamped at both ends. This model results in a nonlinear contribution to the damping. Analytical expressions for the resulting amplitude dependent quality factor and the nonlinear damping parameter in a reduced order model are derived. Large nonlinear damping is predicted when the amplitude of transversal vibration is comparable to the beam thickness, which can be relevant to the beam dynamics.
  • Identification of acoustic sources for bent-axis axial piston motor under
           variable loads
    • Abstract: Publication date: Available online 2 November 2019Source: Journal of Sound and VibrationAuthor(s): Hui Huang, Ganyong Wu, Yongyuan Wu, Shumei Chen The bent-axis axial piston motor is the key actuator of the construction machinery's torque drive and hydrostatic walking. The vibration of the whole motor is not only stimulated by the internal excitation sources, but also affected by the load fluctuation. At the same time, the continuous fluctuation of the load aggravates the evolution of the internal excitation source. Therefore, how to evaluate the impact of load fluctuation on motor vibration and identify the internal excitation source of motor is particularly important. In this paper, the theoretical and experimental research on acoustic sources identification of the bent-axis axial piston motor is carried out. Firstly, according to the structure principle and kinematics characteristics of the motor, the theoretical excitation sources and transfer paths are obtained, and the vibration transmission model based on the excitation sources located in the spindle is established, which can evaluate the effect of load excitation on the overall vibration of piston motor. Further vibration and noise tests under variable loads are completed in the semi-anechoic chamber. The experimental results validate the theoretical vibration transfer model effectively, and reveal the noise sources inside the tested motor under various loads and the transfer of the main noise sources. The maximum vibration amplitude of the outer surface of the motor is shifted from the shell to the backend cover in the process of increasing revs from 500 rpm to 1200 rpm, and the main acoustic source inside the motor is shifted from the eccentricity and unbalance of the spindle to pressure pulsation and flow distribution impact in the process of increasing pressure from 5 MPa to 15 MPa. The data in this paper can be applied to the structure optimization design with load matching, and further provide reference for the follow-up work of reducing vibration and noise under full working conditions.
  • Aeroacoustic simulation of broadband sound generated from low-Mach-number
           flows using a lattice Boltzmann method
    • Abstract: Publication date: Available online 1 November 2019Source: Journal of Sound and VibrationAuthor(s): Kazuya Kusano, Kazutoyo Yamada, Masato Furukawa The present paper demonstrates the capability of a numerical method based on the lattice Boltzmann method (LBM) with wall-resolved grid to predict the broadband sound generated from the turbulent boundary layer at low Mach numbers. The present method is based on the lattice BGK equation with the D2Q9 and D3Q15 models, and a multi-scale approach using hierarchically refined grids is proposed to efficiently and simultaneously capture the multi-scale phenomena of turbulent eddies near walls and far-field sound waves. Numerical instabilities caused by the lack of grid resolution are suppressed with a fourth-order implicit filtering scheme. This numerical method is discussed in two benchmark problems and an application to the prediction of the broadband sound generated from the turbulent boundary layer. First, the computational accuracy and speed of the LBM scheme are assessed with a pulse-propagating problem. The results indicate that the LBM can achieve accuracy comparable to the fourth-order central scheme with the four-stage Runge-Kutta method for the compressible Navier-Stokes (N-S) equations and compute 12.3 times faster. These findings suggest that the LBM is an efficient computational method for aeroacoustic simulations. Second, the proposed method is validated by simulating the Aeolian tone generated by the flow past a circular cylinder at Reynolds number of 150 and Mach number of 0.2. The present simulation is compared with a compressible N-S simulation using a high-order finite difference scheme in terms of the wave profile and the propagation speed of the tonal sound. This validation result suggests that the present method is available for direct aeroacoustic simulations of low-Mach-number flows. Finally, the capability of the present method to predict the broadband sound is demonstrated by conducting a wall-resolved simulation for the turbulent flow generated by a short separation bubble over an isolated airfoil at Reynolds number of 2.0×105 and Mach number of 0.058. This simulation shows a good agreement with measurements of the surface pressure distributions, the wake velocity profiles, and the far-field sound spectrum. In contrast to hybrid approaches based on the incompressible N-S equations, the present method can accurately predict the broadband sound in the high-frequency range by simulating the acoustic scattering on the airfoil.
  • Experimental and numerical characterization of a ceramic matrix composite
           shroud segment under impact loading
    • Abstract: Publication date: Available online 1 November 2019Source: Journal of Sound and VibrationAuthor(s): Florence Nyssen, Nicolas Tableau, Déborah Lavazec, Alain Batailly This work focuses on the experimental and numerical characterization of stress levels within a shroud segment made of ceramic matrix composite (CMC) material undergoing repeated blade contacts. The dedicated experimental set-up consists in a rotating disk with three notched mock blades that impact the shroud segment as they rotate. The underplatform on which the shroud is fixed progressively gets closer to the blades, so that the abradable layer deposited onto the shroud is progressively worn out from a blade revolution to another. Four sensors, located under the shroud segment, are used to record forces during the experiments. Different blade/shroud relative positions are tested, in such a way that impacts may occur at distinct locations. In addition to the experimental tests, a numerical model is built based on both reduced order models of the blade and the shroud segment, in order to numerically predict the forces at the four sensors. This numerical model is first calibrated based on a single reference test case to retrieve the same force magnitude at each sensor. Then, the other tests are simulated using the calibrated model. Predicted contact forces are in good agreement with experimental data, which validates the numerical model. Finally, simulations are carried out considering engine-like conditions, which could not be reproduced using the experimental test bench. The influence of several parameters (radial velocity, impact location, number of blades in contact and angular speed) is analyzed in detail.
  • Experimental and theoretical investigation of rotordynamic characteristics
           of a rigid rotor supported by an active bump-type foil bearing
    • Abstract: Publication date: Available online 31 October 2019Source: Journal of Sound and VibrationAuthor(s): Han-Qing Guan, Kai Feng, Yuan-Long Cao, Ming Huang, Yi-Hua Wu, Zhi-Yang Guo This study aims to investigate the rotordynamic characteristics of a rigid rotor supported by an active bump-type foil bearing (ABFB) with real-time controllable mechanical preload. ABFB is composed of a traditional bump-type foil bearing with controlling substructures that consist of flexure hinges, lever amplifiers and piezoelectric stack actuators (PZTs). The structure realises the adjustment of bearing's mechanical preloads by actively controlling the DC voltage on the PZTs (U). Experimental investigations based on rotordynamic test rig are performed to measure the effects of ABFB on rotordynamic responses of rotor-ABFB system. Combined with the dynamics of the active control structures and modified link-spring model, linear and nonlinear mechanical models of the rotor-ABFB system are established, and the rotordynamic responses of the rotor are predicted. Both the experimental and theoretical results verify the possibility of building active rotor-gas foil bearing systems. Moreover, the effects of rotor unbalance on the rotordynamic responses of the rotor-ABFB system are investigated.
  • Virtual Herschel-Quincke tube using the multiple small resonators and
           acoustic metamaterials
    • Abstract: Publication date: Available online 31 October 2019Source: Journal of Sound and VibrationAuthor(s): Da-Young Kim, Jeong-Guon Ih, Mats Åbom This study is on the practical application of the acoustic metamaterials to the design of a silencer with high acoustic and geometric efficiencies, and negligible pressure drop. The object is to achieve broadband and low-frequency attenuation simultaneously by combining the effects of resonance, periodicity, phase difference, and impedance mismatch. An array of multiple small resonators, which is periodically applied to the wall of a duct, invokes the dispersion of sound propagating in the duct. This phenomenon is implemented to construct a virtual Herschel-Quincke (HQ) tube system. The main duct is split into two parallel ducts of the same length: a rigid duct and a duct with a wall covered by the periodic resonators. For a modelling of sound propagation in a dispersive duct, the phase speed of sound is analytically derived in the presence of a mean flow. Also, the attenuation conditions of the virtual HQ tube are proposed to establish a guideline in selecting the proper design parameters for achieving the required transmission loss (TL) in the desired frequency range. The predicted TL spectra are compared with the test results, for a virtual HQ tube system with 9 identical quarter-wavelength tube resonators, and they generally agree well. With increasing flow speed, the amount of attenuation decreases a bit, but the general spectral characteristics are maintained for M ≤0.1. Based on the same principle, the acoustic metamaterials (AMM) are applied to the practical silencer design to achieve the wide-band sound reduction at low-to mid-frequencies for a given small space. A virtual HQ tube having 26 cells of AMM is tested, of which a cell is composed of 3 types of quarter-wavelength tube resonators. The experiment well validates the predicted TL. The results show that TL is at least 5 dB for a wide frequency range of 230–1000 Hz. The additional volume due to the attachment of the AMM layer is only 40%, while the TL is far larger than that of the simple expansion chamber or the dissipative silencer having the same excess volume.
  • Active vibration control of ship mounted flexible rotor-shaft-bearing
           system during seakeeping
    • Abstract: Publication date: Available online 31 October 2019Source: Journal of Sound and VibrationAuthor(s): Tukesh Soni, A.S. Das, J.K. Dutt Rotor-shaft-bearing system is an integral part of the engine and propulsion system of a ship. Ships are subject to water-waves which cause large rigid body motion of the ship hull involving all six degrees of freedom. This large time-varying ship-motion causes parametric excitation to the flexible rotor mounted on the ship, and may generate high vibratory response of the rotor, although fairly balanced. This paper proposes active control of lateral vibration in such rotors with a suitably placed electromagnetic actuator and compares simulated performance (response amplitude and control current) of different control laws, namely, (i) PD, (ii) PID and (iii) two novel control laws inspired by the mechanical models of a viscoelastic semi-solid. Realistic ship motion during sea-keeping conditions is generated by numerically solving the governing differential equations of motion of a ship under the action of water waves, using indigenously developed code. The equations of motion of the discretized rotor continuum subject to forces from conventional bearings, base motion and the actuator are obtained with respect to a non-inertial reference frame attached to the moving rotor base. Multi-objective optimization of control gains is carried out to obtain minimum rotor-disk response at the expense of the optimum control current. Numerical simulations reveal that the novel control law proposed in (iii) is the most efficient in terms of vibration response and control cost.
  • Response analysis of an accelerating unbalanced rotating system with both
           random and interval variables
    • Abstract: Publication date: Available online 31 October 2019Source: Journal of Sound and VibrationAuthor(s): Chao Fu, Yuandong Xu, Yongfeng Yang, Kuan Lu, Fengshou Gu, Andrew Ball This paper investigates the accelerating up transient vibrations of a rotor system under both the random and uncertain-but-bounded parameters. The Polynomial Chaos Expansion (PCE) coupled with the Chebyshev Surrogate Method (CSM) is used to analyses the propagations of the two categorizes of uncertainties. The output responses will possess the characteristics of both bounded quantities and statistical moments. As a hybrid non-intrusive uncertainty quantification (UQ) procedure, the deterministic rotor model is taken as a black box and will only be executed at some parameter points. A number of uncertain physical parameters are studied and the corresponding transient responses are presented. The accuracy and efficiency are verified by the Monte Carlo simulations (MCS) in combination with the scanning scheme and also other hybrid analysis framework. It will provide guidance for the accurate transient dynamic analysis of engineering problems with hybrid uncertainties.
  • Investigation of gear rattle noise including visualization of vibro-impact
    • Abstract: Publication date: Available online 25 October 2019Source: Journal of Sound and VibrationAuthor(s): Emmanuel Rigaud, Joël Perret-Liaudet This paper presents an experimental study of gear rattle noise induced by vibroimpacts between gear teeth. A specific experimental set-up is designed to analyse the nonlinear dynamic behaviour of a spur gear submitted to input velocity fluctuation. The drag torque, the mean drive gear rotational speed, the velocity fluctuation amplitude and frequency are controlled during experiment. The dynamic transmission error is measured thanks to high resolution optical encoders. The originality of the experimental set-up consists in using a high-speed camera in order to visualize the contact zone and to identify the occurrence of successive impacts between gear teeth. The rattle threshold is identified as a function of velocity fluctuation amplitude and frequency for various operating drag torques and mean rotational speeds. Experiments show very good agreement with the theoretical master curve. Once impacts occur, stationary nonlinear gear dynamic response and rattle noise radiated by the mechanical system are investigated. Most of the time, an almost periodic response is observed with 2 impacts per period. One impact between the active flanks alternates with one impact between the reverse flanks. A contact phase between gear teeth is observed after each impact instead of an instantaneous rebound. The number of successive tooth pairs crossing the meshing zone without any contact between gear teeth varies according to the ratio of the excitation frequency to the rotation frequency. Analytical and numerical works performed using a gear rattle model show good agreement with experiments. Finally, sound pressure emitted from the gear pair is measured. The acoustic power imputable to gear rattle is found to be proportional to the total kinetic energy transferred per second to the system by the successive impacts.
  • On the statistical mechanics of structural vibration
    • Abstract: Publication date: Available online 24 October 2019Source: Journal of Sound and VibrationAuthor(s): R.S. Langley The analysis of the structural dynamics of a complex engineering structure has much in common with the subject of statistical mechanics. Both are concerned with the analysis of large systems in the presence of various sources of randomness, and both are concerned with the possibility of emergent laws that might be used to provide a simplified approach to the analysis of the system. The aim of the present work is to apply a number of the concepts of statistical mechanics to structural dynamic systems in order to provide new insights into the system behaviour under various conditions. The work is foundational, in that it is based on employing the fundamental equations of motion of the system in conjunction with various definitions of entropy, and no recourse is made to emergent laws that are accepted in thermodynamics. The analysis covers closed (undamped and unforced) and open (forced and damped) systems, linear and nonlinear systems, and both single systems and coupled systems. The fact that the system itself can be random leads to a number of results that differ from those found in classical statistical mechanics, where the initial conditions might be considered to be random but the Hamiltonian is taken to be well defined. For example, the occurrence of a stationary state in a closed system normally requires nonlinearity and coarse-graining of the statistical distribution, but neither condition is required for a random system. For coupled systems it is shown that under certain conditions both Statistical Energy Analysis (SEA) and Transient Statistical Energy Analysis (TSEA) are emergent laws, and insights are gained as to the validity of these laws. The analysis is supported by a number of numerical examples to illustrate key points.
  • Vibro-acoustic performance and design of annular cellular structures with
           graded auxetic mechanical metamaterials
    • Abstract: Publication date: Available online 23 October 2019Source: Journal of Sound and VibrationAuthor(s): Qing Li, Deqing Yang An exciting paradigm in the ongoing development of materials is the development of auxetic mechanical metamaterials, which can be flexibly designed to exhibit a unique range of physical and mechanical properties. Inspired by nonuniform or nonhomogeneous metamaterials and structures, annular cellular structures composed of auxetic metamaterials with graded negative Poisson's ratios (NPRs) are studied, and the considered models are divided into two types of configurations: models with graded decreasing NPRs and models with graded increasing NPRs along the radial direction. The spectral element method (SEM) is applied to accurately predict the structural dynamic responses with a limited number of elements and the system scale for arbitrary frequencies. The static stiffness and vibro-acoustic performance of the proposed structures are investigated and compared. The computational results show that the bending stiffness, vibrating mode shapes and deformations, and sound transmission loss (STL) of the considered cellular structures are strongly affected by the arbitrarily patterned graded auxetic metamaterials. Within the studied STL frequency range from 1 to 1500 Hz, optimal designs of the conventional and graded configurations for the maximum STL are obtained for specified tonal and frequency band cases under cylindrical incident sound waves. The results show that the graded configurations have more potential than the conventional ones for optimal acoustic performance and that compared with the graded decreasing NPR models, the graded increasing NPR models exhibit STL increases of 6.73 dB, 1.22 dB, and 2.06 dB for the studied cases. Both the STL and optimal design results indicate the advantages of the graded increasing NPR models for use in acoustic attenuation applications. Thus, graded auxetic metamaterials offer a great opportunity for achieving unusual vibro-acoustic performance and extending the route to obtain an optimized set of physical properties for cellular metamaterials and structures.
  • Automotive wheel and tyre design for suppression of acoustic cavity noise
           through the incorporation of passive resonators
    • Abstract: Publication date: Available online 23 October 2019Source: Journal of Sound and VibrationAuthor(s): Daniel J. O'Boy Tyre cavity noise is a narrow band, high amplitude resonance which occurs when the sound waves in a car tyre oscillate back and forth in one direction with a low loss factor. Manufacturers add damping materials to vehicles, due to the difficulty of reducing the source noise, or mitigating the transmission path from wheel hub to the interior, as part of reducing the overall structure borne noise. When the wheel is rolling, the Doppler effect leads to two characteristic cavity resonance frequencies, which change with speed, loading and temperature. If these couple with a suspension component resonance, a transmission path to the cabin can result. One method to attenuate the sound is by using passive resonators, such as Helmholtz and quarter wavelength resonators. Here, a rapid design method is developed, based around one-dimensional waveguide equations in order to optimise the dimensions and thus the tuned resonant frequency of the wheel based Helmholtz resonators. With three tuned resonators, a reduction in the peak sound amplitude from 103 to 88 dB is possible, over a speed range from 54 km/h to 108 km/h. With five resonators, a reduction from 103 to approximately 87 dB is shown. Thus, the larger number of resonators is better able to attenuate the cavity noise over a larger frequency range.
  • A dynamic model for simulating rubbing between blade and flexible casing
    • Abstract: Publication date: Available online 23 October 2019Source: Journal of Sound and VibrationAuthor(s): Xumin Guo, Jin Zeng, Hui Ma, Chenguang Zhao, Xi Yu, Bangchun Wen Considering the effects of blade rotation and casing flexibility, a new blade-casing rubbing model is proposed. The blade is assumed to be clamped on a rigid disk and simulated by the twisted-shape plate model with a stagger angle, while the casing is simulated by the cylindrical shell model. Considering the influences of the centrifugal stiffening, spin softening and Coriolis force, the equations of motion of the rotating blade are obtained by Hamilton's principle and Galerkin method; the equations are coupled with flexural, radial and swing vibrations. Based on Sanders' shell theory, the cylindrical shell casing with elastic constraints is established where the elastic constraints are described using a set of springs on casing edges. Both models are verified by the result comparisons obtained from the finite element (FE) model or the published literature. The blade-tip is divided into n points along the chordwise direction of the blade, and whether rubbing occurs or not can be determined by judging the position relations between the blade-tip points and the corresponding casing points. The rubbing-induced vibration responses between the rotating blade and the flexible casing are also compared with those obtained from the rubbing model with the rigid casing and the FE model with the flexible casing. The results show that, compared with the rigid casing model using lumped mass points, the cylindrical shell casing model can consider the flexibility of the casing, and the nodal diameter vibration of the casing induced by rubbing can be observed. Moreover, both the rubbing force and the vibration response of the blade contacting with the flexible casing will decrease compared with those contacting with the rigid casing. Finally, based on the proposed model, the effects of rotational speed, blade shape, blade-tip geometry and asymmetric support boundary of casing on the rubbing responses of the system are also analyzed.
  • An exact analytical solution for free in-plane vibration of sector plates
           with simply supported radial edges
    • Abstract: Publication date: Available online 22 October 2019Source: Journal of Sound and VibrationAuthor(s): Yunbo Yuan, Hongliang Li, Donghua Wang, Chen Liu, Yibin Guo, Wanyou Li In this paper, an exact analytical solution is proposed to investigate the free in-plane vibration of sector plates. The highly complex and coupled differential equations of in-plane vibration motion are decoupled by invoking Helmholtz decomposition. The method of separation of variables is used to solve the resulting uncoupled Helmholtz equations. Applying the boundary conditions at both radial edges, the compatible eigenvalue problems for sector plates are obtained. Then, applying the boundary conditions at inner and outer circumferential edges, the corresponding characteristic equations can be solved to obtain the natural frequencies and the associated mode shapes. The results from the proposed method agree very well with the results from the available literature and the FEM. Significant influence of the boundary conditions and the geometric parameters on the free in-plane vibration characteristics of sector plates is investigated and addressed. The superficial frequency veering “aberration” between neighboring modes is discussed and found in fact to be an eigenvalue crossing phenomenon. It is proved that for a sector plate, only with simply supported radial edges, there exists the exact analytical solution. The proposed exact analytical solution can provide not only the detailed physical characteristics of the free in-plane vibration of sector plates but also the benchmark for further study.
  • On the numerical simulations of amplitude-adaptive impact dampers
    • Abstract: Publication date: Available online 21 October 2019Source: Journal of Sound and VibrationAuthor(s): Tunc Yüzbasioglu, Jimmy Aramendiz, Alexander Fidlin Two impact dampers are analysed and compared with respect to their effectiveness for vibration reduction. Estimations of nonlinear system behaviour are derived using only well-known solutions for a linear dynamic vibration absorber. Critical parameter values separating domains with qualitatively different system behaviours are found. Using numerical simulations, the estimations are verified and the influence of each system parameter on the vibration amplitudes is investigated individually. Each of these systems exhibits advantages in the suppression of particular resonances, because they react either to the absolute or relative motion within the system.
  • A stochastic Functional Model based method for random vibration based
           robust fault detection under variable non–measurable operating
           conditions with application to railway vehicle suspensions
    • Abstract: Publication date: Available online 18 October 2019Source: Journal of Sound and VibrationAuthor(s): T.-C.I. Aravanis, J.S. Sakellariou, S.D. Fassois The problem of random vibration based robust fault detection under variable and non–measurable Environmental and Operating Conditions (EOCs) is considered, and a novel stochastic Functional Model (FM) based method is postulated. It is a data–driven method, of the Statistical Time Series (STS) type, and aims at overcoming the well known drawbacks of available methods by achieving high detection performance while eliminating their drawbacks, such as the need for measurable EOCs, for measurement of a high number of vibration signals for proper training, for subjective judgement in selecting method parameters, and for high dimensional non–convex optimization procedures. The method is based on representing the system dynamics, under any set of EOCs, in a proper feature space, within which the healthy dynamics are represented by a proper healthy subspace constructed via a Functional Model. Fault detection is then based upon determining, at a certain risk level, whether or not the current dynamics resides within the healthy subspace. The method's assessment is achieved via simulation results with a case study pertaining to fault detection in a railway vehicle suspension under variable payload, with high detection performance, clearly exceeding that of an alternative Principal Component Analysis (PCA) based method.
  • The statistical errors in the estimated correlation function matrix for
           operational modal analysis
    • Abstract: Publication date: Available online 18 October 2019Source: Journal of Sound and VibrationAuthor(s): Marius Tarpø, Tobias Friis, Christos Georgakis, Rune Brincker Given the random vibration of a linear and time-invariant system, the correlation function matrix is equivalent to free decays when the system is excited by Gaussian white noise. Correlation-driven Operational Modal Analysis utilises these properties to identify modal parameters from systems in operation based on the response only. Due to the finite length of the system response, the correlation function matrix must be estimated and this introduces statistical errors. This article focuses on the statistical errors due to this estimation process and the effect it has on the envelope and zero crossings of the estimated correlation function matrix. It is proven that the estimated correlation function matrix is a Gaussian stochastic process. Furthermore, it is proven that the envelope of the modal correlation function matrix is Rice distributed. This causes the tail region of the correlation function to become erroneous - called the noise tail. The zero crossings are unbiassed, but the random error related to the crossings increases fast in the noise tail. The theory is tested on a simulated case and there is a high agreement between theory and simulation. A new expression for the minimal time length is introduced based on the bias error on the envelope.
  • Noise radiated from a periodically stiffened cylindrical shell excited by
           a turbulent boundary layer
    • Abstract: Publication date: Available online 17 October 2019Source: Journal of Sound and VibrationAuthor(s): Laurent Maxit, Oriol Guasch, Valentin Meyer, Mahmoud Karimi This work proposes a semi-analytical method to model the vibroacoustic behavior of submerged cylindrical shells periodically stiffened by axisymmetric frames and excited by a homogeneous and fully developed turbulent boundary layer (TBL). The process requires the computation of the TBL wall-pressure cross spectral density function and the sensitivity functions for stiffened cylindrical shells. The former is deduced from an existent TBL model and the latter are derived from a wavenumber-point reciprocity principle and a spectral formulation of the problem. The stiffeners' dynamic behavior is introduced in the formulation through circumferential admittances that are computed by a standard finite element code using shell elements. Four degrees of freedom are taken into account for the coupling between the shell and the stiffeners: three translation directions and one tangential rotation. To investigate the effect of the stiffeners on the radiated noise, two case studies are considered. The first one examines a fluid-loaded cylindrical shell with regularly spaced simple supports. The influence of Bloch-Floquet waves and the support spacing on the noise radiation are highlighted. The second case study inspects the fluid-loaded cylindrical shell with two different periodic ring stiffeners, namely stiffeners with T-shaped and I-shaped cross-sections. Their influence on the vibroacoustics of the shell is thoroughly analyzed.
  • Evaluating reduced order models of curved beams for random response
           prediction using static equilibrium paths
    • Abstract: Publication date: Available online 17 October 2019Source: Journal of Sound and VibrationAuthor(s): C.I. Van Damme, M.S. Allen, J.J. Hollkamp Thin curved structural components are susceptible to dynamic snap-through when subjected to the high amplitude aerodynamic loading that is present in extreme environments. In order to estimate the life of the structures, time simulations must extend over many seconds so that the statistical response due to the random loading environment can be adequately characterized. In order to compute the geometrically nonlinear response of these structures in a reasonable time, Reduced Order Models (ROMs) have been developed that reduce the computational burden dramatically. However, the accuracy of a ROM can vary drastically depending on how it is created, specifically depending on which modes are included within the basis set and the magnitude of the static loads used to estimate the nonlinear stiffness coefficients in the ROM. This work presents a procedure to check that a ROM is accurate in dynamic snap through prior to computing the dynamic response. The Riks method is used to compute the static equilibrium path, or force-displacement behavior, for both the FE model and the ROM, and by comparing these one gains insight into the character of the ROM. Two curved beams are studied to validate the procedure and we identify load levels and mode sets that produce accurate ROMs for these structures. The ROMs are further validated by computing the dynamic response, and the results show that, for these two structures, if the ROM accurately predicts the static snap through behavior of the model to a uniformly distributed static load, then it also correctly reproduces the dynamic response to a uniform pressure that varies randomly in time.
  • Contact mechanics and friction processes in ultrasonic wire bonding -
           Basic theories and experimental investigations
    • Abstract: Publication date: Available online 17 October 2019Source: Journal of Sound and VibrationAuthor(s): Yangyang Long, Jens Twiefel, Jörg Wallaschek Even though ultrasonic (US) wire bonding has been a popular interconnection technique in electronic packaging industry for decades, the contact and friction conditions during the bonding processes have not been well understood. In this work, the relative motion at the wire/substrate interface and the tool/wire interface, and the influences of oxides and microwelds on the friction at the wire/substrate interface are brought together to systematically and comprehensively analyze the contact and friction at the two interfaces. Specifically for the analysis at the wire/substrate interface, the contact was divided into three different areas where different oxide removal and microweld formation condition exists. The theoretical analysis was then validated by real-time observations from both side and bottom view. Both analyses show that in the beginning stage, the tool and the wire are well coupled. The wire gross-slides on the substrate and the most substantial friction takes place in the inner peripheral region. The shift of the tool equilibrium position was experimentally observed during this stage. As the process goes on, the contact area between the wire and the substrate gets larger. Within the contact area, the oxide layer is broken into particles and then transported to the peripheral contact region. Microwelds are formed in the oxide-free areas. Sliding friction and microweld connections coexist at the wire/substrate interface. As more oxides are removed and more microwelds are formed, the relative displacement at the wire/substrate interface becomes smaller while the relative displacement at the wire/tool interface becomes larger. Finally, microwelds cover the majority of the contact. The understanding on the contact and friction of US wire bonding leads to a potential enhancement of processes in industry production.
  • Robust uncertainty quantification in structural dynamics under scarse
           experimental modal data: A Bayesian-interval approach
    • Abstract: Publication date: Available online 17 October 2019Source: Journal of Sound and VibrationAuthor(s): Maurice Imholz, Matthias Faes, Dirk Vandepitte, David Moens The accurate prediction of the dynamic behaviour of a complex component or system is often difficult due to uncertainty or scatter on the physical parameters in the underlying numerical models. Over the past years, several non-deterministic techniques have been developed to account for these model inaccuracies, supporting an objective assessment of the effect of these uncertainties on the dynamic behaviour. Still, also these methods require a realistic quantification of the scatter in the uncertain model properties in order to have any predictive value. In practice, this information is typically inferred from experiments. This uncertainty quantification is especially challenging in case only fragmentative or scarce experimental data are available, as is often the case when using modal data sets. This work therefore studies the application of these limited data sets for this purpose, and focuses more specifically on the quantification of interval uncertainty based on limited information on experimentally obtained eigenfrequencies. The interval approach, which is deemed to be the most robust against data insufficiency, typically starts from bounding the data using the extreme values in the limited data set. This intuitive approach, while of course representing the experiments, in general yields highly unconservative interval estimates, as the extreme realisations are typically not present in the limited data set. This work introduces a completely new approach for quantifying the bounds on the dynamic properties under scarce modal data. It is based on considering a complete set of parametrized probability density functions to determine likelihood functions, which can then be used in a Bayesian framework. To illustrate the practical applicability of the proposed techniques, the methodology is applied to the well-known DLR AIRMOD test case where in a first step, the bounds on the experimental eigenfrequencies are estimated. Then, based on a calibrated finite element model of the structure, bounds on the frequency response functions are estimated. It is illustrated that the method allows for a largely objective estimation of conservative interval bounds under scarce data.
  • Demodulation technique to identify nonlinear characteristics of
           vibro-acoustic NDT measurements
    • Abstract: Publication date: Available online 15 October 2019Source: Journal of Sound and VibrationAuthor(s): A. Carcione, P. Blanloeuil, M. Veidt A novel approach for nonlinear ultrasonics is presented which uses the demodulated response of a nonlinear vibro-acoustic response signal. The demodulation process is similar to quadrature demodulation process used in telecommunications. It is shown that the demodulation method provides an alternative approach for the analysis of nonlinear behavior compared to the analysis of frequency spectra or other techniques. The proposed method suggests that a representative reconstruction of the time-domain nonlinearity behavior of the system can be obtained. The paper provides theoretical background to the technique as well as experimental validation. The proposed method is demonstrated for the analysis of four different types of contact acoustic nonlinear interfaces. It is shown that the demodulated waveforms are consistent with the expected mechanical behavior of different interfaces. The results suggest that this method can provide more insight into the nonlinear behavior of a system compared to conventional spectral amplitude analysis techniques.
  • Extracting torsional band gaps and transient waves in phononic crystal
           beams: Method and validation
    • Abstract: Publication date: Available online 11 October 2019Source: Journal of Sound and VibrationAuthor(s): Kuo-Chih Chuang, Zhi-Wen Yuan, Y.Q. Guo, Xu-Feng Lv Due to an absence of proper measuring techniques, torsional waves/vibrations in one-dimensional phononic crystals (PCs) or elastic metamaterials are usually theoretically or numerically studied without experimental validations. This work proposes a measurement method capable of extracting torsional band gaps and transient torsional waves from the total responses of PC and metamaterial beams. Specifically, a pair of point-wise self-demodulated fiber Bragg grating (SFBG) displacement sensors, which can be arranged at points very close to each other on a thin PC beam, is utilized along with the proposed extraction method. The SFBGs are symmetrically set up at two locations about the central line on the surface of the PC beam. The torsional band gaps and the transient torsional waves are extracted from the differential responses of the two SFBGs, in which the common bending waves are cancelled out. In addition to the torsional behaviors, the bending waves can also be extracted from the summation responses of the two SFBGs. We first examine the dynamic linearity of the SFBGs. Then, steady-state detection of the torsional and bending band gaps of a PC beam is performed. Finally, a cantilever PC beam subjected to an eccentric steel ball impact, whose loading history is recorded by a pair of polyvinylidene fluoride (PVDF) films, is investigated to demonstrate the extraction of the torsional/bending bandgap and waves from the early short time transient responses. The feasibility of the proposed torsional (or bending) extraction method is justified by the method of reverberation-ray matrix (MRRM), which is capable of providing “pure” torsional (or bending) behaviors of the PC beam. With the proposed extraction method, we also observe surface localized modes in the transmission of the PC beam, which are strongly related to the arrangement of the constituent components with different impedances in the unit cells. We believe that the proposed extraction method for torsional wave, along with the SFBG sensing technique and the MRRM, can provide future researchers with measurement and analysis methods to validate their designs of torsional phononic crystals or metamaterials.
  • Corrigendum to “Local bending stiffness identification of beams using
           simultaneous Fourier-series fitting and shearography” [J. Sound Vib. 443
           (2019) 764–787]
    • Abstract: Publication date: Available online 10 October 2019Source: Journal of Sound and VibrationAuthor(s): Filip Zastavnik, Rik Pintelon, Mathias Kersemans, Wim Van Paepegem, Lincy Pyl
  • Comments on “Free vibration of functionally graded beams and frameworks
           using the dynamic stiffness method [J. Sound Vib. 422(2018) 34–47]”
    • Abstract: Publication date: Available online 9 October 2019Source: Journal of Sound and VibrationAuthor(s): A.A. Popov
  • Commentary on, “Discussion on ‘Free vibration of functionally graded
           beams and frameworks using the dynamic stiffness method’ by Banerjee et
           al., Journal of Sound and Vibration 442 (2018) 34–47.”
    • Abstract: Publication date: Available online 4 October 2019Source: Journal of Sound and VibrationAuthor(s): J.R. Banerjee, A. Ananthapuvirajah
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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