Vibration Of Plates Research Articles

Broadband low-frequency sound insulation of a metamaterial plate with inertial amplification

The recent development of Inertia Amplification (IA) acoustic metamaterial (AMM) opens a new venue for insulating low-frequency sound waves. This differs from conventional approaches that rely excessively on the structural density of the insulator and, therefore, lead to prohibitively heavy structures. The IA-AMM acquires a large effective density and a broad flexural bandgap by amplifying the inertia of many small mass elements periodically distributed in its unit cells, thus holding great promise as an effective yet lightweight solution for low-frequency sound insulation. This paper explores this possibility through numerical and experimental investigations. A semi-analytical model of an IA-AMM plate is developed by combining analytical equations characterizing the kinematics of an IA mechanism and FEM equations governing the vibration of the host plate. Based on this model, sound transmission characteristics of the plate under various sound incidences are analyzed with different amplification angles. By comparing with a locally resonant AMM plate, we found that the IA-AMM plate's sound transmission losses (STLs) are significantly and systematically improved over a wide frequency range of 116–544 Hz. To understand the underlying physics, the band diagram of the IA-AMM plate is calculated, which indicates the formation of a flexural bandgap covering the frequencies of the improved STL. The velocity contour of the plate at the center frequency of this bandgap also reveals much-suppressed vibration velocity amplitudes and a dipole-like sound radiation directivity, further explaining the observed enhancement of the sound insulation ability. Numerically predicted improvement of sound insulation is finally confirmed by experiments.

An Investigation into the Free Vibration of Intact and Cracked FGM Plates

In this study, the linear free vibration of intact and cracked functionally graded material plates is investigated numerically and experimentally. The experimental work is limited to the isotropic materials. The numerical work is based on finite element, where a code is developed to obtain the natural frequencies of intact plates based on the first-order shear deformation theory (FSDT) using MATLAB software. Also, a model of through-cracked FGM plate is developed using ANSYS Workbench with the help of APDL coding. The material properties of the plates under study are graded in one, two, and three directions. The novelty of this study emerges through its examination of the synergistic impacts resulting from variations in FGM material properties, crack length, crack orientation, and crack location. These effects are comprehensively discussed in the results section. The result of the present model shows that the use of three-directional FGM reduces the natural frequency compared with the other cases of two-directional and unidirectional FGM. Also, the results show that the effect of FGM gradient on the frequency of intact and cracked plate is high when the gradient index n < 3 . The present paper results are useful for the design of FGM plates especially when cracks exist.

Flow-induced reconfiguration and cross-flow vibrations of an elastic plate and implications to energy harvesting

We numerically study flow-induced vibrations (FIV) of an elastic cantilevered plate in a cross-flow configuration. The plate is kept upright in an open domain with a fixed bottom end. Such a configuration eliminates energy losses in the wall boundary. Due to allowed vortex shedding from its bottom end, the resulting novel dynamics of the fluid-structure interaction (FSI) system is explored. An in-house sharp-interface immersed boundary method-based flow solver, coupled with a Saint-Venant Kirchhoff material model-based open-source finite element solver, is employed. Two sets of simulations were carried out in two-dimensional Cartesian coordinates at Reynolds number of 100 for a wide range of reduced velocity (UR), by performing a parametric sweep of dimensionless Young’s modulus (E) and mass ratio (M). In general, FIV characteristics of the plate are similar to the transverse vortex-induced vibration of an elastically-mounted cylinder. The plate deforms to a curved mean position depending on E and M and exhibits angular oscillations. In particular, the following FIV regimes are obtained with increasing UR: initial excitation, lock-in with the first mode, desynchronization after the first lock-in, lock-in with the second mode, and desynchronization after the second lock-in. During lock-in, the plate oscillation and vortex shedding frequency are closer to the first or second mode natural frequency of plate. A larger angular amplitude and increased energy exchange between the structure and fluid characterize the lock-in. We quantify the modal contributions of Euler-Bernoulli modes in the plate’s vibration response with a curved mean position. The spatiotemporal variation of energy exchange between the fluid and plate is analyzed to understand the observed plate dynamics. The flow physics of the wake is discussed using wake patterns, vortex formation length, and vortex strength. Drag over the plate reduces due to flow-induced reconfiguration and strongly correlates with these parameters. Lastly, based on the spatial distribution of strain energy density over the plate, we present a potential design for an ambient fluid energy harvester to harness the plate’s vibration energy with optimized piezoelectric patching. The optimum location and height of a piezoelectric patch on the plate for different cases are reported.

Mechanism of noise reduction caused by thickening top plate for high-speed railway box-girder bridge

For the high-speed railway concrete box-girder bridge, thickening the top plate can effectively reduce the structural noise radiation caused by moving trains. However, the noise reduction mechanism for thickening top plate has not been investigated. This mechanism is systematically studied in this paper by employing a train-track-bridge spatially coupled dynamics model and an acoustics boundary element model of the box-girder bridge. The results demonstrate that the top plate is the dominant noise source for the concrete box-girder bridge. Thickening top plate can significantly reduce the noise radiation capacity of the box-girder bridge, mainly through three mechanisms: (1) reducing the local modal shapes and vibrations of top plate, (2) decreasing the acoustic radiation efficiency, and (3) redistributing the train-induced vibration in the bridge. Furthermore, these three aspects collectively determine the total amount and spatial distribution of the noise radiation from the box-girder bridge due to moving trains. It is crucial to comprehensively these three aspects for the low-noise design of box-girder bridge.

Acoustic scattering from a wave‐bearing cavity with flexible inlet and outlet

In this article, we substantiate the appositeness of the mode‐matching technique to study the scattering response of bridging elastic plates connecting two flexible duct regions of different heights. We present two different solution schemes to analyze the structure‐borne and fluid‐borne radiations in the elastic plate‐bounded waveguide. The first scheme supplements the mode‐matching technique with the so‐called tailored‐Galerkin approach that uses a solution ansatz with homogeneous and integral parts corresponding to the vibrations of the bridging elastic plate and the cavity, respectively. In the second scheme, we supplement the mode‐matching technique with the modal approach wherein the displacement of the bridging elastic plate is projected onto the eigenmodes of the cavity. To handle the non‐orthogonality of the eigenfunctions, we invoke generalized orthogonality relations. An advantage of the proposed mode‐matching schemes is that they provide a convenient way of incorporating a variety of edge conditions on the joints of the plates, including clamped, pin‐joint, or restraint connections. The numerical analysis of the waveguide scattering problems substantiates that edge connections on the joints have a significant impact on the scattering energies and transmission loss. Furthermore, it appears that the transmission loss and structural vibration attenuation in the expansion chamber may be improved by adjusting chamber dimensions and excitation modes.

Free vibration of a bi-layered composite plate of a piezoelectric semiconductor and a piezoelectric dielectric

We study the free vibration of a piezoelectric bi-layered plate composed of a piezoelectric semiconductor (PS) layer and a piezoelectric dielectric (PD) layer. The macroscopic theory of a PS consisting of the conventional theory of piezoelectricity and the drift-diffusion theory of semiconductors is used. The nonlinear equations for drift currents of electrons and holes are linearized for small perturbation of carrier density. The first-order zigzag approximation for in-plane displacements and electric potential through the thickness of each layer is used. Interfacial continuity of the displacement, the transverse shear stress, and the electric potential between the PS layer and the PD layer is ensured, which is very important and also experienced by layered structures. The number of independent unknown variables is reduced from 11 to 5 by using the interfacial continuity and the zero shear stress conditions at the top and bottom surfaces. The governing equation and corresponding boundary condition are derived using Hamilton’s principle. An analytical solution of a simply supported composite plate is obtained. The effects of steady-state electron density, axial force, and the geometric parameters on the vibration frequency and modes are discussed. The obtained results may be useful for further theoretical analysis of PS composites and practical application of piezotronic devices made from PS and PD materials.

Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson’s ratio

Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson’s ratio

Free vibration analysis using dynamic stiffness method and first-order shear deformation theory for a functionally graded material plate

In the current simulation work, free vibration analysis of the levy-type plates made of functionally graded material (FGM) has been carried out using first-order shear deformation theory (FSDT) and dynamic stiffness method (DSM). It is assumed that for functionally graded (FG) plates, density and elastic modulus continuously vary along the transverse direction of the plates following power law distribution. The governing differential equation for the free vibration of a rectangular FG plate and its associated natural boundary conditions are formulated using Hamilton's principle under the assumption of displacement fields following FSDT. Eigen-values for different vibration modes are obtained by implementing the Wittrick-William algorithm on the DSM of the FG plate. Results using the current method have been validated from previously published literature to check their accuracy level. The validation analysis shows the current results are in good agreement with the published literature, which gives us enough confidence to carry out further investigation. The effects of different plate parameters on the frequency such as material gradient index, aspect ratio, and boundary conditions are investigated and discussed in detail.

Study of the Velocity and Direction of Piezoelectric Robot Driven by Traveling Waves

Self-running piezoelectric robots have the advantages of being low cost, high load ratio and fast speed of operation, as well as showing few limitations in confined spaces or for underwater applications. Controlling the speed of motion of such robots by adjusting the Standing Wave Ratio (SWR) along the vibration plate of the robot is important. Compared to the conventional dual-mode excitation method which is based on the adjustment of the excitation frequency, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> , a novel SWR-based control method, using the adjustment of the temporal phase shift, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ</i> , has been first derived by the authors. It has been found that the travelling wave component could be maximised using both methods, either by setting the value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> to the root mean square of the two adjacent modal frequencies, or by programming <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ</i> to have a sum of π when added to the spatial phase difference. It can be seen that using the ‘θ-based’ traveling wave control method, smoother motion and higher resolution of the motion speed is achieved. In this research, by using the novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ</i> -based method to drive the robot, its motion characteristics, such as voltage-speed, load capacity and ability to move on different surface materials, have been tested through a series of experiments carried out and reported.

Enhancement of vibrational characteristics of rotating CFRP composite tapered plates reinforced by graphene nanoparticles

AbstractIn the present study, the dynamic behavior of rotating carbon fiber reinforced polymer (CFRP) composite tapered plates reinforced with graphene nanoparticles has been investigated using a finite element (FE) formulation. The mechanical properties of CFRP laminates containing 0–0.5 wt% graphene nanoparticles were assessed using ASTM standard tests. The experimental dynamic analysis was conducted on CFRP and graphene reinforced CFRP composites under cantilever end conditions. The first‐order shear deformation theory (FSDT)‐based FE model was developed using MATLAB software to obtain the natural frequencies of the graphene reinforced CFRP plates. The validity of the FE results is compared with literature, and it shows excellent agreement for composite structures. Furthermore, parametric analysis is performed to explore the influence of wt% of graphene, rotating speed, setting angle, and ply thickness on the dynamic responses of graphene reinforced CFRP tapered plates.Highlights Effects of graphene reinforcement in CFRP composites are investigated. The mechanical characteristics were evaluated using ASTM standards. FSDT is employed to model the rotating tapered graphene‐CFRP plates. Vibration behavior of graphene‐CFRP composites is studied experimentally. Effects of various factors on the vibrations of the CFRP plates are studied.

Free vibration and nonlinear dynamic response of sandwich plates with auxetic honeycomb core and piezoelectric face sheets

This article analyses the nonlinear dynamic behavior and the free vibration of a piezoelectric auxetic honeycomb sandwich plate resting on a Pasternak elastic substrate. The plate includes two face sheets of piezoelectric material and an auxetic honeycomb core with a negative Poisson ratio. The first-order shear deformation plate theory, together with the von Kármán type nonlinear strain-displacement relationship, is used to establish the nonlinear equations of motion. Linear electric potential change with piezoelectric layer thickness is assumed. Two types of boundary conditions, namely immovable and movable simply supported, are considered. The displacement-time and acceleration-displacement curves under dynamic loads are determined by using the Galerkin and Runge-Kutta fourth-order methods. Verification examples have been performed and confirmed the accuracy of the model. Finally, several novel investigations have been conducted to evaluate the effect of material, geometrical parameters, and elastic substrate coefficients on the frequency and nonlinear dynamic characteristics of piezoelectric auxetic honeycomb sandwich plates for both open-circuit and closed-circuit operation.

Comment to the article M.V. Shitikova, V.V. Kandu, A.I. Krusser, On nonlinear vibrations of an elastic plate on a fractional viscoelastic foundation in a viscoelastic medium in the presence of the one-to-one internal resonance, Journal of Sound and Vibration 549 (2023) 117564

Comment to the article M.V. Shitikova, V.V. Kandu, A.I. Krusser, On nonlinear vibrations of an elastic plate on a fractional viscoelastic foundation in a viscoelastic medium in the presence of the one-to-one internal resonance, Journal of Sound and Vibration 549 (2023) 117564

Commentary to discussion of ‘On nonlinear vibrations of an elastic plate on a fractional viscoelastic foundation in a viscoelastic medium in the presence of the one-to-one internal resonance’ by M.V. Shitikova, V.V. Kandu, A.I. Krusser, Journal of Sound and Vibration 549 (2023) 117564

Commentary to discussion of ‘On nonlinear vibrations of an elastic plate on a fractional viscoelastic foundation in a viscoelastic medium in the presence of the one-to-one internal resonance’ by M.V. Shitikova, V.V. Kandu, A.I. Krusser, Journal of Sound and Vibration 549 (2023) 117564

Numerical study on the static bending and forced vibration of triclinic plate with arbitrary boundary conditions

Numerical study on the static bending and forced vibration of triclinic plate with arbitrary boundary conditions

Warping deformation of the track slab and their influence on the interlayer stiffness and vibration transmission characteristics of the unit ballastless track

The unit ballastless track partially segments the concrete track bed in the longitudinal direction, and relieves the concrete temperature stress by isolating the upper and lower layers. However, the layer isolation leads to the incompatible deformation of the upper and lower track structures under the effect of the temperature gradient. A large temperature gradient on the track slab will cause local contact between layers, the contact area between layers will then decrease, thus leading to “stiffness softening” between layers. When the vehicle passes, the contact area between layers will gradually increase, which, in turn, leads to “stiffness hardening”. The analysis results show that the greater the design stiffness between layers, the more significant the “stiffness softening” effect will be under the temperature gradient. When k0 = 400 × 106 (N·m−1)·m−2 and Tg = 90 °C·m−1, the interlayer stiffness decreases by 88%.The simulation analysis results of the wheel-drop impact test show that under a positive temperature gradient, the peak value of rail vibration acceleration increases, and the peak value of the track slab and base plate vibration acceleration decreases. The greater the stiffness designed between layers, the more obvious the influence will be. With the increase of the positive temperature gradient, the vibration acceleration of the rail and the track slab will be reduced in the 1–30 Hz and 40–100 Hz frequency domains. With the increase of the negative temperature gradient, the vibration acceleration of the rail in the 4–10 Hz, 20–50 Hz frequency domains, and the vibration acceleration of the track slab in the 70–200 Hz frequency domains will be increased. A large positive temperature gradient inhibits the transmission of high-frequency vibrations above 40 Hz to the substructure, while a negative temperature gradient inhibits the transmission of low-frequency vibrations within 30 Hz and 70–200 Hz to the substructure. A positive temperature gradient is beneficial to restrain the downward transmission of low-frequency vibration. When k0 = 200 × 106 (N·m−1)·m−2, the low-frequency vibration transmission loss of the track slab to the base plate is close to 0 dB without temperature gradient, but the positive temperature gradient increases the transmission loss by about 10 dB, the greater the temperature gradient, the higher the transmission loss of the track slab to the base plate under high stiffness.

Effects of graphene-platelets reinforcement on the free vibration, bending, and buckling of porous functionally-graded metal-ceramic plates

This paper presents a first investigation of the mechanical behavior of porous functionally-graded material (FGM) plates reinforced with graphene platelets (GPls) nanomaterial. As a main purpose, we extend the research on GPls incorporation from single-component matrix materials to porous metal-ceramic FGMs. Four different through-thickness distributions of GPls and porosities were investigated. The effective elastic modulus of GPls-reinforced FGM was calculated using the Halpin-Tsai homogenization model, and the effect of porosities on elastic properties was considered by an exponential model that is more accurate than the common rule of mixture. A recent hyperbolic higher-order plate theory that satisfies the traction-free boundary conditions and a parabolic variation of shear stresses was used to model kinematics. The influence of various parameters was studied after method validation, and it was revealed that GPls not only can improve the stiffness and mechanical response of FGM plates, but can also eliminate the inherent transverse anisotropy of FGMs and uncouple the static response when dispersed in proper distribution pattern. This effect will result in zero mid-plane extension in bending conditions, in a similar behavior to isotropic plates.

An improved MITC3 element for vibration response analysis of piezoelectric functionally graded porous plates

The main goal of this paper is to improve the mixed interpolation of tensorial components triangular (MITC3) by using the edge-based smoothed finite element method (ES-FEM), so-called ES-MITC3, for analyzing the vibration of piezoelectric functionally graded porous (p-FGP) plates subjected to dynamic loading. The material properties of the FGP core vary through thickness with uneven porosity distribution. Besides, the linear relationship between the electric potential and the thickness of the piezoelectric sublayer is taken into account. A closed-loop control algorithm is employed to actively control the vibration of p-FGP plates, through feedback from displacement and velocity. The performance of the proposed method is verified through comparative examples. Finally, the authors hope that the present method can be effectively applied to many smart material models in a multiphysics environment and contribute to understanding texture control by piezoelectric materials through numerical results.

Nonlinear parametric excitation and dynamic stability of auxetic honeycombs core with CNTRC face sheets sandwich plate

This study aims to analyze the Nonlinear vibration and instability of a sandwich plate with an Auxetic Honeycomb core and a Carbon Nanotube Reinforced Composite (CNTRC) face layer on a viscous elastic foundation under parametric excitation. In the analytical model, the Hamilton principle and nonlinear strain-displacement relations determined by Von Karman theory and the first shear deformation plate theory (FSDT) are used. The governing equations are solved using the Galerkin method, which involves expanding the displacement field based on orthogonal functions. Once the displacement field has been expanded, a multiple-scale method is used to solve the equation of motion. The results show that the bifurcation diagrams and stability of sandwich plates depend on several parameters, including the geometric dimension of the honeycomb core, the material properties of the CNTRC face layer, and the temperature increment. The results of this study will likely be helpful in optimizing the design of sandwich plates for engineering applications, including the aerospace and automotive industries, where sandwich structures are widely utilized because of their high strength-to-weight ratios and excellent energy absorption capabilities.

Two-photon 3D printing diaphragm-integrated ring waveguide coupler for ultrasound detection.

We demonstrate a diaphragm-integrated ring waveguide coupler fabricated by the two-photon direct laser wring technique as an ultrasonic sensor, which is integrated on an optical fiber tip. The device consists of a micro-ring waveguide with a diameter of 5 µm functionalized as an optical fiber tip light reflection mirror and a straight waveguide connecting a diaphragm. The evanescent field coupling can be realized between the two waveguides, and the coupling efficiency can be changed due to the variation of the coupling gap induced by ultrasound. Accordingly, the light reflection can be changed. Based on the plate vibration theory, the vibration frequency can be changed through optimizing the diaphragm size. The experiments show that the device exhibits a high sensitivity and low noise equivalent acoustic signal level of 1.07 mPa/Hz1/2 at 100 kHz, which has great potential in various acoustic wave sensing applications.

The Effect of Cracks on the Free Vibration of a Plate with Parabolic Thickness

This paper uses first-order shear deformation theory and the finite element method to analyze the vibrations of rectangular plates with one or more cracks. The study investigated the influence of cracks (length, angle of inclination), the number of cracks, and the ratio of plate thickness to the natural vibration frequency of the plate, using phase field simulation. Plate thickness varies nonlinearly with the parabolic function. The results of the proposed method were compared with reputable studies to verify its reliability. In addition, some pictures of the characteristic vibration patterns of the plate with varying thickness are presented when cracks appear.