Wave Propagation In Plate Research Articles

An efficient model for wave propagation of temperature-dependent E-FGM plates resting on viscoelastic foundation

The present work shows the plate's wave propagation behavior made of exponent-law-based functionally graded materials (E-FGM) supported by viscoelastic foundations. In extreme thermal environments, where the E-FGMs are considered highly effective, the temperature influences the composite plate's properties. Therefore, this present study aims to investigate the wave propagation of the E-FGM plates by considering the temperature-dependent effective properties as functions of the position across the thickness and the thermal increase. The governing equations of the E-FGM plate are obtained by employing a simple higher-order shear deformation theory (HSDT) and utilizing the Hamilton principle. An eigenvalue problem is formulated to determine the principal wave propagation frequency. The effects of viscoelastic parameters on E-FGM plates' phase velocities under uniform thermal changes are investigated in detail. The results indicate that introducing metal-ceramic mixtures in the plate would lower the phase velocity in the plate. Furthermore, increasing a uniform temperature in the plate would deteriorate the foundation and plates and, therefore, result in lower velocity and less stiffness.

Controlling elastic wave propagation in plates using magic squares

A magic square is defined as a square array of distinct positive numbers arranged such that the sum along the horizontal, vertical, and main diagonal directions are the same, which is called a magic number. Previously, we leveraged the magic square concept to create a new class of phononic structures whose dispersion behavior can be tuned without altering their global mass and stiffness. In this study, we study the dispersion behavior of a thin plate with non-structural mass arranged in a magic square pattern. The plate unit cell is partitioned into nine portions and individual point masses are embedded at the center of each portion. Our results show that the magic square mass-embedded plate provides a low-frequency out-of-plane bandgap whose widths can be controlled while maintaining the global mass of the plate structure. Additionally, we investigate a magic plate concept by applying different densities at each portion associated with the magic square patterns. Our preliminary results show that the magic density distribution results in the emergence of polarized bandgaps and provides a possibility of altering the plate modal frequency without altering the mode shape or the global mass.

The local radial basis function collocation method for elastic wave propagation analysis in 2D composite plate

In this paper, the local radial basis function collocation method (LRBFCM) is applied to simulate the in-plane elastic wave propagation in composite plate. In order to reduce the influence caused by large aspect ratio, an improved LRBFCM based on direct method is developed so that the governing equations can be numerically decoupled by using bilinear nodes in different directions. Several numerical examples are given to demonstrate the accuracy and efficiency of the proposed technique in simulating the elastic wave propagation with large aspect ratio.

Propagation of fundamental Lamb modes along the non-principal axes of strain-stiffened soft compressible plates: A numerical investigation.

This paper numerically investigates the propagation of elastic plate waves along the non-principal directions in a prestretched compressible material described by the Gent model of hyperelasticity. We formulate the elastic tensor and the underlying wave equations in the Lagrangian space by employing the theory of nonlinear elasticity together with the linearized incremental equations. An extension of the Semi-Analytical Finite Element (SAFE) method is discussed for computing the dispersion characteristics of the two fundamental guided wave modes. The predictive capabilities of the numerical framework are established using the previously published data for a weakly nonlinear as well as hyperelastic material models. Using the numerical framework, we then bring out the effects of applied prestretch, orientation of the propagation direction, and material parameters on the dispersion characteristics of the fundamental Lamb modes. A limiting case of the neo-Hookean material model is first considered for elucidating such implicit dependencies, which are further highlighted by considering the strain-stiffening effect captured through the Gent material model. Our results indicate the existence of a threshold prestretch for which the Gent-type material can encounter a snap-through instability; leading to the change in the dispersion characteristics of the fundamental symmetric Lamb mode.

Lamb waves propagation in nematic elastomer plates by the Legendre polynomial series approach

The Lamb waves in nematic elastomer plates are investigated by adopting the viscoelasticity theory in the hydro-dynamic (low frequency) limit. The Legendre polynomial series approach is employed to obtain the complex wave number solutions to characterize the wave propagation and attenuation. Some unique Lamb wave characteristics are revealed. Results show that the cutoff frequencies of all Lamb modes vanish due to the high viscoelasticity. Except for A0 mode, each mode has a minimal attenuation frequency. Besides, the attenuation of nematic phase is thousands of times greater than the isotropic phase, which would be significant in designing damping applications.

TRANSFORMATION OF A LONGITUDINAL ELASTIC WAVE INTO A POCHHAMMER WAVE

The finite element method in a dynamic formulation was used to characterize the propagation of longitudinal elastic waves in cylindrical plates and Pochhammer waves in rods. It was shown that in compact bodies first only one longitudinal wave propagates until unloading waves from the side surfaces begin to interact, and then two types of longitudinal elastic waves propagate simultaneously. In rods, a longitudinal elastic wave propagates at the initial stage. Over time, the influence of unloading from the side surfaces of the rod leads to the simultaneous propagation of two types of elastic waves: a longitudinal elastic wave and a Pochhammer wave. Using aluminum as an example, the range of geometric parameters was determined for nearly compact bodies, whose elastic properties cannot be evaluated by ultrasonic methods.

Theoretical analysis of guided waves propagation in periodic piezoelectric plates with shunting circuits

The tunable manipulation of guided waves in plates brings out great potential applications in engineering practices, and the electromechanical coupling effects of piezoelectric material with shunting circuits have exhibited powerful tunability and flexibility for guided wave propagation. In this paper, a theoretical model is established to analyze the guided wave propagation in one-dimensional periodic piezoelectric plate constructed from a periodic array of anisotropic piezoelectric materials under periodic electrical boundary conditions. The extended Stroh formalism incorporating with the plane wave expansion method is developed to transform the wave motion equations of the periodic piezoelectric plate into a linear eigenvalue system, and a more concise and elegant solution of generalized displacement and generalized stress can be derived. There are various dispersion relations in terms of the altering electrical boundary conditions to be acquired, if the thin electrodes with shunting circuits are attached periodically to both surfaces of the piezoelectric plate. Analytical results show that the coupling of the local electric resonant mode and propagating elastic wave modes can induce hybridization bandgaps, and the bandgaps of Lamb waves and SH waves in the piezoelectric plate can be tuned by designing appropriate material polarization orientations and shunting circuits. In addition, the Bragg bandgaps can also be influenced by the external circuits. Results indicate that the proposed theoretical model can effectively analyze the performances of guided waves in periodic piezoelectric plate and provide useful theoretical guidance for designing smart wave control devices.

Theoretical and experimental analysis of guided wave propagation in plate-like structures with sinusoidal thickness variations

Guided waves have attracted significant attention for non-destructive testing (NDT) and structural health monitoring (SHM) due to their ability to travel relatively long distances without significant energy loss combined with their sensitivity to even small defects. Therefore, they are commonly used in damage detection and localization applications. The main idea of incorporating guided waves in NDT and SHM is based on processing the received signals and appropriate interpretation of their characteristics. A great amount of research devoted to diagnostics of plate-like structures considers specimens with constant thickness, which significantly facilities the diagnostic process. In such a case the velocity is also assumed to be constant. However, the developed diagnostic methods should be applicable, especially for the structures exposed to an aggressive environment, excessive load, or unfavorable weather conditions, etc., when the probability of damage occurring is much higher. In such cases, the assumption about the uniform thickness alongside the propagation path cannot be applied in every case. Thus, the present study is focused on wave propagation in metallic plates with variable thickness. The results of theoretical, numerical and experimental investigations of antisymmetric Lamb mode propagation in aluminum plates with a sine-shaped surface are presented. In the first step, the influence of non-uniform thickness distribution on wave velocity has been described. Next, the inverse problem aimed at shape reconstruction based on time of flight (ToF) analysis and spatially varying wave velocity was solved and compared with the standard dispersion curve-fitting method.

Effects of the external magnetic field on propagation of thickness-twist waves in inhomogeneous plates

Effects of the external magnetic field on propagation of thickness-twist waves in inhomogeneous plates

Numerical and experimental investigation of guided ultrasonic wave propagation in non-uniform plates with structural phase variations

The article presents the results of numerical and experimental investigations of guided wave propagation in aluminum plates with variable thickness. The shapes of plate surfaces have been specially designed and manufactured using a CNC milling machine. The shapes of the plates were defined by sinusoidal functions varying in phase shift, which forced the changes in thickness variability alongside the propagation path. The main aim of the study is to analyze the wave propagation characteristics caused by non-uniform thickness. In the first step, the influence of thickness variability on the time course of propagating waves has been analyzed theoretically. The study proves that the wave propagation signals can be determined based on knowledge about the statistical description of the specimen geometry. The histograms of thickness distribution together with the a priori knowledge of the dispersion curves were used to develop an iterative procedure assuming that the signal from the previous step becomes the excitation in the next step. Such an approach allowed for taking into account the complex geometry of the plate and rejecting the assumption about the constant average thickness alongside the propagation path. In consequence, it was possible to predict correctly the signal time course, as well as the time of flight and number of propagating wave modes in specimens with variable thickness. It is demonstrated that theoretical signals predicted in this way coincide well with numerical and experimental results. Moreover, the novel procedure allowed for the correct prediction of the occurrence of higher-order modes.

Design and Robustness Evaluation of Valley Topological Elastic Wave Propagation in a Thin Plate with Phononic Structure

Based on the concept of band topology in phonon dispersion, we designed a topological phononic crystal in a thin plate for developing an efficient elastic waveguide. Despite that various topological phononic structures have been actively proposed, a quantitative design strategy of the phononic band and its robustness assessment in an elastic regime are still missing, hampering the realization of topological acoustic devices. We adopted a snowflake-like structure for the crystal unit cell and determined the optimal structure that exhibited the topological phase transition of the planar phononic crystal by changing the unit cell structure. The bandgap width could be adjusted by varying the length of the snow-side branch, and a topological phase transition occurred in the unit cell structure with threefold rotational symmetry. Elastic waveguides based on edge modes appearing at interfaces between crystals with different band topologies were designed, and their transmission efficiencies were evaluated numerically and experimentally. The results demonstrate the robustness of the elastic wave propagation in thin plates. Moreover, we experimentally estimated the backscattering length, which measures the robustness of the topologically protected propagating states against structural inhomogeneities. The results quantitatively indicated that degradation of the immunization against the backscattering occurs predominantly at the corners in the waveguides, indicating that the edge mode observed is a relatively weak topological state.

Tunable asymmetric transmission of Lamb waves in piezoelectric bimorph plates by electric boundary design

The multi-mode and dispersion natures of elastic guided waves bring big challenges for wave manipulation, and also provide more possibilities for smart device design. In this study, a piezoelectric bimorph plate connected to a periodic arrangement of electric circuits is proposed, and both propagating and evanescent guided Lamb waves are investigated through the complex band structure resulting form using different shunting capacitor or inductor distributions. Results show that keeping and breaking the symmetry of the electric boundary condition can, respectively, lead to decoupling or hybridizing of multi-mode Lamb waves. Accordingly, the asymmetric transmission at a desired frequency can be realized by combining the symmetric and asymmetric electric boundary conditions. Harmonic analysis shows that numerical results are in good agreement with the prediction of complex band structure. Actively changing the electric boundary conditions can be used for guided wave propagation in piezoelectric bimorph plates to easily control the system without changing the structure’s geometry. The framework presented herein offers enhanced capabilities for controlling guided wave propagation for engineering applications and to develop nondestructive testing techniques.

Construction of a mathematical model of lamb wave propagation in a steel pipeline with a protective outer coating

THE PURPOSE. Adapt the method of measuring the propagation of Lamb waves in thin two-layer plates to the study of the dependence of the phase velocity on the technical condition of pipelines with a protective outer coating. To perform a modification of the numerical-analytical algorithm for measuring the thickness of the coating and areas of non-adhesion of materials in thin two-layer plates for vibroacoustic diagnostics of technical pipelines. To investigate the propagation of a symmetric Lamb wave in a steel pipeline with a protective outer coating. METHODS. To solve the problem of localizing damage to technical pipelines, traditional methods of non-destructive testing based on vibroacoustic diagnostics are considered. RESULTS. Work on the construction of a mathematical model of the dependence of the propagation of the phase velocity of the Lamb wave on the thickness of the object under study has been carried out. The numerical analysis of the measurements was carried out using the example of thin two-layer segments of pipelines. The presence of changes in the thickness of the pipeline is taken as the effect of material defects on the propagation parameters of the Lamb wave mode. CONCLUSION. A numerical-analytical method for calculating the propagation of a symmetric Lamb wave mode in a thin segment is presented. The dependence of the propagation velocity of Lamb waves on the segment thickness is demonstrated. Based on the described technique, it seems possible to estimate not only the thickness of the segment and the area of non-adhesion of the layers, but also the total area of the defective area. This will allow in the future to record the relative changes in the thickness of the walls of pipelines to determine changes in the physical properties of the material or the presence of a defect.

Wave Propagation in Smart Sandwich Plates with Functionally Graded Nanocomposite Porous Core and Piezoelectric Layers in Multi-Physics Environment

This research provides a mathematical model and solution for investigating wave propagation in graphene platelets (GPLs)-reinforced functionally graded (FG) metal foam plates integrated with piezoelectric actuator and sensor layers resting on an orthotropic visco-Pasternak medium in magneto-electro-thermo environment. The FG porous nanocomposite core and the actuator piezoelectric layer are exposed to steady magnetic and electric fields, respectively. The electric potential between two piezoelectric layers is governed by a proportional-derivative controller. The Halpin–Tsai micromechanics model and the Kelvin–Voigt model are adopted to express the effective elastic modulus of the FG porous nanocomposite core and material viscoelasticity of the core and piezoelectric layers, respectively. The governing equations of smart FG porous nanocomposite plates under thermal environment are derived grounded on the refined third-order shear deformation theory. Upon the validated theoretical model, the wave velocities and frequencies in plates are obtained by solving governing equations analytically. Finally, the effects of material viscoelasticity, porosity distribution and coefficient, GPL distribution and weight fraction, the plate and GPL geometries and external environment on wave propagation characteristics are demonstrated comprehensively. This work provides guidance on tunable control of wave propagation in smart sandwich plates affected by complex external environments.

Localized waves in elastic plates with perturbed honeycomb arrays of constraints.

In this paper, we study wave propagation in elastic plates incorporating honeycomb arrays of rigid pins. In particular, we demonstrate that topologically non-trivial band-gaps are obtained by perturbing the honeycomb arrays of pins such that the ratio between the lattice spacing and the distance of pins is less than 3; conversely, a larger ratio would lead to the appearance of trivial stop-bands. For this purpose, we investigate band inversion of modes and calculate the valley Chern numbers associated with the dispersion surfaces near the band opening, since the present problem has analogies with the quantum valley Hall effect. In addition, we determine localized eigenmodes in strips, repeating periodically in one direction, that are subdivided into a topological and a trivial section. Finally, the outcomes of the dispersion analysis are corroborated by numerical simulations, where a time-harmonic point source is applied to a plate with finite arrays of rigid pins to create localized waves immune to backscattering.This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.

Propagation of elastic waves in metamaterial plates with various lattices for low-frequency vibration attenuation

Elastic wave propagation characteristics of elastic metamaterial plates embedded scatterer with various lattices are explored numerically and experimentally in this study, for the attenuation of in-plane longitudinal and out-of-plane flexural waves in the subwavelength frequency region. Firstly, the mathematical models of the elastic metamaterial plates are established, and the dispersion relations are derived by the plane wave expansion (PWE) method based on Bloch's theorem. Furthermore, the applicability of the irreducible Brillouin zone (IBZ) for different lattices is also investigated through iso-frequency contours. The analysis of the bandgap formation mechanism indicates that the proposed metamaterial plates can enlarge the bandgaps (BGs) in the low-frequency range by coupling Bragg and local resonance BGs. Moreover, the influences of the scatterer shapes, geometric and material parameters on the BGs are investigated, and which combination of parameters has positive significance for opening low-frequency broadband is also discussed. The results show that the vibration transmittance obtained by experiment and numerical calculation is in good agreement with the predicted results of band structures. Therefore, the elastic metamaterial plates should be promising in the application of low-frequency wave mitigation.

On-chip valley phononic crystal plates with graded topological interface

In this work, we construct on-chip valley phononic crystal plates by building up triangular silicon pillars on the silicon plate. We introduce the graded interface sliding for two typical interfaces ψBA and ψAB, by modulating the horizontal lattice constant in a selected region in PC plate. Based on simulation and laser ultrasonic technique, we present the frequency range evolution of topological edge states from the gapless feature to gapped one. We demonstrate the displacement distribution of topological edge states in two graded interfaces, magnifying numerically the topological rainbow phenomena. In particular, we characterize the plate wave propagation through both types of graded interfaces, observe the abnormal refraction pattern behind the truncated interfaces, and underline abnormal refraction to the splitting of wave vector in PC plate. Our graded interfaces provide new clue to control elastic wave propagation based on valley degree of freedom.

Impact of Micromechanical Approaches on Wave Propagation of FG Plates via Indeterminate Integral Variables with a Hyperbolic Secant Shear Model

The aim of this paper is to analyze the impacts of micromechanical approaches on the wave propagation of a functionally graded (FG) plate via indeterminate integral variables with hyperbolic secant shear displacement models. This model is established based on a high-order theory and a new displacement field with four unknowns introducing indeterminate integral variables with a secant hyperbolic shear function. Six micromechanical approaches are applied to approximate the effective material properties of an FG plate, namely Voigt’s model, Reuss’ model, Hashin–Shtrikman’s lower, and upper bound models, Tamura’s model, and the LRVE model. The volume fractions are supposed to change corresponding to the power-law and sigmoid. By applying Hamilton’s principle, general formulae of the wave propagation were obtained to get the wave modes and phase velocity curves of wave propagation in FG plates, with the impact of Voigt’s, Reuss’, Hashin–Shtrikman’s bounds, Tamura’s, and LRVE explicit micromechanical models.

Localised Waves In Elastic Thin-Walled Structures

In this paper the authors provide a review of our investigations pertaining to localized bending waves in thinwalled structures. The authors also present the statements and analytical results fortwo new problems related to bending edge wave propagation in homogeneous infinite plate reinforced by inclusions, modelled as elastic beam or elastic plate.

Determination of stepped plate thickness distribution using guided waves and compressed sensing approach

Guided waves recently have attracted significant interest as a very promising research area. The signals registered by a specially designed sensor network are processed to assess the state of the tested structure. Despite the constant development of novel damage detection algorithms employing guided waves, the phenomenon of wave propagation still needs detailed recognizing and understanding for the further progress of non-destructive wave-based methods. Special attention is paid to guided waves in plate-like structures, but the majority of considered cases concern plates with constant thickness. However, in the real world, we often deal with specimens with variable thickness. The thickness variability of the specimen is often forced to fulfill the construction requirements and optimize stress distribution or is the result of degradation i.e. corrosion. Thus, the development of NDT methods forces the need of considering specimens with complex geometry and the problem of wave propagation in waveguides with variable thickness is crucial for improving novel as well as so far proposed algorithms.The article presents the results of the analytical, numerical and experimental analysis of wave propagation in plates with variable thickness. The analysis concerns the influence of thickness distribution of plate structure on wave velocity, the time course wave packet and amplitude. Moreover, the novel approach based on constrained convex optimization for determining the plate thickness distribution has been proposed and verified during numerical and experimental campaigns.