Wave Propagation In Plate Research Articles

Peculiarities of Lamb Waves Propagating in Functionally Graded Layers

Propagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by the modified Cauchy six-dimensional formalism. For arbitrary transverse inhomogeneity a closed form dispersion equation is derived. Dispersion relations for materials with different kinds of inhomogeneity are obtained and compared.

Topological interface and corner states of flexural waves in metamaterial plates with glide-symmetric holes

This study investigates the topological localization and propagation of flexural waves in metamaterial plates with perforated holes exhibiting glide symmetry. The dispersion relations of flexural waves in this mechanical system exhibit four-fold Dirac degeneracies at the M point of the Brillouin zone. By properly adjusting the rotation angles of the perforated holes, these degeneracies can be lifted up to create omnidirectional bandgaps, enabling nontrivial topological phases. Both numerical and experimental results demonstrate multiple topological states of flexural waves in the developed elastic metaplates, including dual-band helical interface states and anisotropic interface/corner states. The simple perforated metaplates with glide-symmetric holes provide novel, manufacturable platforms for the flexible manipulation of topological flexural waves, greatly facilitating potential applications such as energy harvesting and signal enhancement.

Guided elastic wave propagation in elastic metamaterial plate with periodic array of interfacial crack-like voids

Abstract A special kind of elastic metamaterials with periodic unit-cells composed of two layers with internal crack-like voids situated at the interfaces between two neighboring sub-layers is studied. To investigate experimentally guided waves propagation in EMMs with arrays of voids, several specimens with periodic arrays of crack-like voids have been manufactured using additive manufacturing techniques. The elastic waves have been excited by a rectangular piezoelectric transducer bonded at the surface of the specimen, while the wave-fields on the surface of the EMM specimen are measured by a laser Doppler vibrometer. The dispersion characteristics are investigated using the matrix pencil method and band-gaps are observed experimentally.

3D wave dispersion analysis of graphene platelet-reinforced ultra-stiff double functionally graded nanocomposite sandwich plates with metamaterial honeycomb core layer

This research addresses the three-dimensional thermomechanical wave propagation behavior in sandwich composite nanoplates with a metamaterial honeycomb core layer and double functionally graded (FG) ultra-stiff surface layers. Due to its potential for high-temperature applications, pure nickel (Ni) is preferred for the honeycomb core layer, and an Al2O3/Ni ceramic-metal matrix is preferred for the surface layers. The functional distribution of graphene platelets (GPLs) in three different patterns, Type-U, Type-X, and Type-O, in the metal-ceramic matrix with a power law distribution provides double-FG properties to the surface layers. The mechanical and thermal material characteristics of the core and surface layers, as well as the reinforcing GPLs, are temperature-dependent. The pattern of temperature variation over the plate thickness is considered to be nonlinear. The sandwich nanoplate’s motion equations are obtained by combining the sinusoidal higher-order shear deformation theory (SHSDT) with nonlocal integral elasticity and strain gradient elasticity theories. The wave equations are established by using Hamilton’s principle. Parametric simulations and graphical representations are performed to analyze the effects of honeycomb size variables, wave number, the power law index, the GPL distribution pattern, the GPL weight ratio, and the temperature rise on three-dimensional wave propagation in an ultra-stiff sandwich plate. The results of the analysis reveal that the 3D wave propagation of the sandwich nanoplate can be significantly modified or tuned depending on the desired parameters and conditions. Thus, the proposed sandwich structure is expected to provide essential contributions to radar/sonar stealth applications in air, space, and submarine vehicles in high or low-temperature environments, protection of microelectromechanical devices from high noise and vibration, soft robotics applications, and wearable health and protective equipment applications.

Effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular plate with variable hybrid foundation

Engineering structures' heterogeneity and porous-auxetic features generate some prominent effects on their thermo-mechanical behavior. In addition, initial stress and heat wave propagation also play important roles in the mechanical behavior of FGM structures. Therefore, this paper investigates the effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular/annular plates with variable hybrid foundations. The one-dimensional transient hyperbolic heat conduction equation is modeled using the Cattaneo-Vernotte (C-V) theory and numerically solved using the Crank-sNicolson (C-N) finite difference scheme. Besides, a mathematical model of the other governing equations is extracted based on the classical thermoporoelasticity theory and semi-analytically solved by employing the state-space method and differential quadrature technique. Numerical examples are provided to illustrate the findings of this investigation graphically. The results reveal that the grading indices, and thermal relaxation time have a significant effect on heat wave propagation in the FG circular plate. Initial stress, porosity, and auxeticity also play an important role in its thermoelastic behavior.

Wave packet enriched finite element for accurate modelling of thermoelectroelastic wave propagation in functionally graded solids

A wave packet enriched finite element (FE) formulation featuring electrothermomechanical coupling is presented for solving two-dimensional wave propagation problems in functionally graded elastic and piezoelectric media. The FE equations for the Lord-Shulman and Green-Lindsay theories of generalized piezothermoelasticity are derived, where the standard Lagrangian interpolation functions of the temperature, electric potential, and displacement field variables are extrinsically enriched with element-domain sinusoidal wave-packet functions and are solved using the Newmark–β direct time integration. The effective properties of the functionally graded material (FGM) are computed using the volume-fraction-based micromechanics models, the Mori-Tanaka model and Voigt's rule of mixture (ROM) model. A variety of wave propagation problems, including the mechanically and electrically excited high-frequency Lamb wave propagation in FGM plates, impact waves in FGM bars, and thermal shock waves in functionally graded piezoelectric cylinders, are solved using the present formulation, and results are validated with available solutions. The efficacy of the current solution in comparison with the conventional FE is evaluated for all the studied problems. The effect of the inhomogeneity parameter on the transient wave behaviour is also presented for all the problems. The results of the Mori–Tanaka model are compared with those of the widely used ROM.

Nonlinear thermoelastic wave propagation in general FGM sandwich rectangular plates

The present work is dedicated to investigating the thermoelastic wave propagation behavior of sandwich rectangular plates (SRP) made of functionally graded material (FGM). The main contribution lies in the partial modification of basic theoretical expressions and solution methods to improve the accuracy of practical system models. An analytical model with three types of general configurations is established. The porosity distribution in FGM layers depends on the degree of mixture of the constituent materials, with the FGM layers without porosity taken as a reference model. The effect of porosity within FGMs is addressed through a refined analytical formulation of material properties, and the temperature-dependent material properties of FGM sandwich structures (FGMSS) maintain continuity through the thickness. This improved framework introduces a porosity function encompassing three distinct structural and geometrical functions: the core-to-thickness ratio (CTR), porosity volume fraction (PVF), and porosity distribution function (PDF). It is worth mentioning that the theoretical expressions maintain good continuity and reliability under the influence of thermal conditions and system parameters of the proposed structures. Furthermore, considering the generation of thermal strain energy (TSE) caused by thermal expansion of the structure in the normal direction, an improved analytical approach for determining TSE in rectangular plate structures is then investigated by introducing the Green's nonlinear strain (GNS). Hamilton's principle is applied to derive the wave motion equations and analytical solutions for the wave dispersion relations are derived. Furthermore, accurate numerical simulation is performed and the solution is verified with data available in published resources. In addition, we present a systematic parametric analysis to examine the effects of porosity, configuration, power-law exponent (PLE), PVF, CTR, temperature, and wave number on the thermoelastic wave propagation behavior of FGMSRP.

Bayesian data-driven framework for structural health monitoring of composite structures under limited experimental data

Ultrasonic-guided waves can be used to monitor the health of thin-walled structures. However, the run of experimental damage tests on materials like carbon fiber-reinforced plastics can be impractical and costly. Instead, numerical models can be used to create hybrid datasets to train machine learning algorithms, integrating data from numerical and experimental tests. This paper presents a Bayesian-driven framework to compensate for limited experimental data regarding Lamb wave propagation in composite plates. Using Bayesian inference, the framework updates a numerical finite element model, considering observed uncertainties by sampling posterior probability density functions for input parameters using Markov–Chain Monte Carlo simulations with the Metropolis-Hastings algorithm. A neural network surrogate model speeds-up these simulations, leading to a model that replicates the uncertain experimental setup. This model then generates data to augment true experimental data. Finally, a one-dimensional convolutional neural network is trained on a three different datasets to analyze Lamb wave signals and assess damage. Comparing training strategies shows the hybrid dataset augmented by samples generated by the updated FE model gives the most accurate damage size predictions.

Ice plate deformation and cracking revealed by an in situ-distributed acoustic sensing array

Abstract. Studying seismic sources and wave propagation in ice plates can provide valuable insights into understanding various processes, such as ice structure dynamics, migration, fracture mechanics and mass balance. However, the harsh environment makes it difficult to conduct in situ dense seismic observations. Consequently, our understanding of the dynamic changes within the ice sheet remains insufficient. We conducted a seismic experiment using a distributed acoustic sensing (DAS) array on a frozen lake, exciting water vibrations through underwater airgun shots. By employing an artificial intelligence method, we were able to detect seismic events that include both high-frequency icequakes and low-frequency events. The icequakes clustered along ice fractures and their activity correlated with local temperature variations. The waveforms of low-frequency events exhibit characteristics of flexural-gravity waves, which offers insights into the properties of the ice plate. Our study demonstrates the effectiveness of an DAS array as an in situ dense seismic network for investigating the internal failure process and dynamic deformation of ice plates such as the ice shelf, which may contribute to an enhanced comprehension and prediction of ice shelf disintegration.

Size parameter calibration of nonlocal strain gradient theory based on molecular dynamics simulation of guided wave propagation in aluminum plates

The nonlocal strain gradient theory (NSGT) describes long-range interatomic interactions and higher-order strain gradients by introducing size parameters. However, the NSGT is constrained in studying the elastic wave propagation problems due to the difficulty in obtaining the precise size parameters. In this paper, the molecular dynamics (MD) simulations of the elastic wave propagation in the aluminum nano-plate are conducted, and the size parameters in the NSGT are calibrated based on the MD simulation results. The MD simulation process is divided into three stages: relaxation, excitation, and free vibration analysis. The embedded atom method is used to describe the interactions between the metal atoms. During the MD simulations, appropriate boundary conditions and excitation methods are proposed to obtain the group velocities of the elastic bulk, Lamb and SH waves. In addition, based on the three-dimensional (3D) elasticity theory and analytical integration Legendre polynomial method, the theoretical dispersion curves of the elastic wave propagation in the NSGT model are obtained. It is found that both the nonlocal theory and the NSGT can predict the guided elastic wave group velocity, and the NSGT prediction and MD simulation can be well matched when the size parameters are restricted to a certain calibrated regional band. The vibration of atoms in the Lamb wave propagation process is more complex than that in the SH wave propagation, leading to a more substantial size effect on the Lamb wave dispersions.

Hybrid experimental/computational approach to Time Reversal source localization in thin plates using image source method

Standard approaches to source localization usually rely on trilateration, using signals detected at multiple receiving points, with further research focused on improving localization robustness and reducing the number of sensors required. Time Reversal (TR) is a valid alternative, however it is often difficult to define a reliable hybrid (computational/experimental) approach, particularly in the case of plates where dispersive properties of the propagating waves play a crucial role to obtain focusing. In this paper, we present an analytical method that describes wave propagation in thin plates, accounting for edge reflections and dispersive properties, and validate it by comparison to experimental data. The Image Source Method (ISM), employed and extended in this study, provides an analytical means of Green's function computation through multiple edge-reflected propagation paths and proves to be reliable and fast to study propagation of Lamb waves in thin plates. A one-channel hybrid TR approach based on ISM is also proposed, utilizing experimental signals transferred to the model for backpropagation computation. In particular, the determination of the optimal signal duration to be time-reversed is discussed.

Nondestructive corrosion degradation assessment based on asymmetry of guided wave propagation field

The article presents the results of numerical and experimental investigation of guided wave propagation in steel plates subjected to corrosion degradation. The development of novel procedures allowing for the assessment of the corrosion degradation level is crucial in the effective diagnostics of offshore and ship structures that are especially subjected to aggressive environments. The study’s main aim is to investigate the influence of surface irregularities on wave propagation characteristics. The paper investigates wavefront asymmetry caused by the non-uniform thickness of damaged specimens. In the first step, the influence of thickness variability on the symmetry of the wave field has been investigated numerically. The corroded plates with variable degrees of degradation have been modeled using the random fields approach. The degree of degradation (DoD) varied from 0% to 40%. In the next step, the developed method was examined during experimental tests performed on specimens subjected to accelerated corrosion degradation. The experimental tests were conducted for intact and for corroded plates characterized by a DoD of 10%. It is demonstrated that the new approach based on wave field analysis can be used in structural state assessment.

Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base

The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite elastic thin plate with a circular orifice of radius r0 lying on a rough base. Considering the friction forces and their influence on the sample of wave propagation in extended rods or thin plates is important for calculating the stress–strain state in them and the size of the area of motion. An exact analytical solution of a nonlinear boundary value problem for tangential stresses and velocities is obtained in quadratures by the Laplace transform, with respect to time. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance r* from the center of the orifice, and an elementary formula is given for this distance (the case of tangential shock stresses suddenly applied to the orifice boundary is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the stopping (trailing) wave fronts are calculated. After passing them, a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual stresses is established in the region r0≤r≤r*. For the first time, a precise analytical solution was obtained for the boundary value problem of the propagation of elastic shear waves in an infinite isotropic space with a cylindrical cavity, when a tangential shock load is set on its surface.

Effect of viscoelastic coating on Lamb wave propagation in plates

Dispersion curves for elastic multilayer plates are useful to describe the behavior of guided wave modes in composite materials. They provide information to set up the appropriate launching conditions of the guided waves for assuring high scanning distances with sensitivity. This paper applies an efficient Gauss-Lobatto-Legendre (GLL) collocation method to formulate the Scaled Boundary Finite Element Method SBFEM to estimate the dispersion curves and wave structure in metallic plates with viscoelastic coatings. This formulation is quite efficient because it discretize the cross-section of each layer with only one spectral element. As a result, a global stiffness matrix is obtained by assembling the stiffness matrices of each layer. The formulation leads to a first-order eigenvalue problem by implementing the Z coefficient matrix that can be efficiently solved to compute the (ω, k) couples that guarantee the wave modes propagating in the structure. The estimated phase velocity and group velocity curves for coated and free plates show a small frequency shifting exhibited in some modes, with predominant displacement in the viscoelastic layer of the wave displacement profile.

Investigation of guided wave propagation in nanoscale layered periodic piezoelectric plates based on Eringen's nonlocal and strain gradient theory

This paper investigates the dynamic propagation behavior of guided waves in nanoscale media composed of alternating layers of piezoelectric phases. The study employs Eringen's nonlocal and strain gradient theories to derive equations for symmetric wave propagation and the scattering relations of guided waves perpendicular to these structures. Dispersion curves are calculated and plotted to compare these theories, considering the influence of nanoscale size-effect, volume ratio of constituent layers, and material length scale. Using the strain gradient theory, the paper explores the impact of length scale parameters on the propagation behavior of horizontally polarized guided waves in an alternating layer structure of nanoscale piezoelectric material, specifically nanoscale piezoelectric laminates. The analysis involves calculating localization factors and dispersion curves to analyze the effects of size-effect and length scale parameters on wave propagation and band structures. Additionally, the study plots and analyzes changes in mechanical displacement and electrical potential, followed by an investigation and discussion of nanoscale size effects and the effects of the material's length scale parameter on dispersion curves and conversion modes within specific regions. The results highlight that the length scale effect parameter significantly impacts the mode conversion zones and band gap structures, more so than the NLPE continuum theory suggests. As the strain gradient parameter increases, these zones shift towards higher wavenumbers and to the right . Furthermore, introducing the length scale factor results in a substantial decrease in both the formation of conversion zones and the density of dispersion curves.

Peculiarities of Optoacoustic Excitation and Propagation of Plate Waves in Thin-Walled Оbjects

Peculiarities of Optoacoustic Excitation and Propagation of Plate Waves in Thin-Walled Оbjects

Application of Damage Detection of Metal Structure Lamb Wave Modal Superposition Imaging Based on Scanning Laser Vibration Measurement

Metal structural plates are extensively used in various engineering structures due to their high strength, high-temperature resistance, toughness, and plasticity. However, they are susceptible to damage from external loads and impacts over time. The current Lamb wave detection methods suffer from dispersion and multimodal effects, leading to ineffective identification of damage information. In this paper, we investigate Lamb wave propagation in steel structure plates with flat-bottomed holes using a sinusoidal modulation five-peak wave signal. Finite element numerical models are developed, and an experimental platform is constructed using steel and aluminum boards. Experimental data is collected using a Scanning Laser Doppler Vibrometer (SLDV, PSV-500, Polytec Inc., Baden-Württemberg, German). The results demonstrate that, under the same frequency, the damage reflection energy for different modes is distinct. By fusing the data from the two modes, more accurate damage imaging results are obtained in the frequency-wavenumber (f-k) domain compared to single-mode imaging. Furthermore, experiments are conducted to locate damage in a steel board with a through hole and an aluminum plate with double flat-bottomed holes, confirming the feasibility of the proposed algorithm in isotropic plates.

Numerical Analysis of Vibration Attenuation and Bandgaps in Radially Periodic Plates

ObjectivePeriodic configuration of mechanical and civil structures has shown great potential for noise and vibration reduction. However, the use of Cartesian coordinates in studying periodicity effects in elastic structures overlooks the benefits of radially periodic configurations when dealing with wave propagation in large flexible plates disturbed by a small source area. This paper presents an easy-to-use numerical approach to predicting bandgap characteristics in polar coordinates.MethodologyTo demonstrate the vibration-attenuation effect, we consider a circular radially periodic plate model. We use an adapted Wave Finite-Element method in numerical experiments to demonstrate the existence of the attenuation effect. To verify the numerical results, we apply an adapted Floquet theory to polar coordinates.Results and ConclusionsOur findings indicate that theoretical and numerical results are in excellent agreement considering a new parameter that introduces the distance from the origin. The adapted Wave Finite-Element approach and Floquet theory presented here demonstrate their potential to model more complex structures in polar coordinates.

Numerical Simulations in Ultrasonic Guided Wave Analysis for the Design of SHM Systems—Benchmark Study Based on the Open Guided Waves Online Platform Dataset

Structural health monitoring (SHM) strategies based on ultrasonic guided waves are very promising regarding thin-walled lightweight structures. To study the performance of such systems, validated numerical analysis tools have to be used. For that procedure, a benchmark between two numerical methods will be presented. The first promising approach is the elastodynamic finite integration technique (EFIT). Miscellaneous research shows that its capability of capturing wave characteristics and interactions is advanced in various media and structures, including thin-walled composites. The second approach employs conventional shell-type finite elements following the Reissner–Mindlin theory for modelling layered composite structures. The advantage of using such finite element methods (FEM) is their high availability in general purpose simulation tools. As a reference model, the measurement data coming from the Open Guided Waves Project (OGW) was taken into account. The OGW dataset provides the experimental data of ultrasonic guided wave propagation in carbon fiber composite plates with an additional omega stringer. By using this contribution, this experiment was reproduced by simulation. The paper presents the results of a validation and motivates further research, such as in research related to the probability of detection analysis and numerical performance.

Investigation of shock wave propagation and water cavitation in a water-filled double plate subjected to underwater blast

Water-filled double hulls are a prevalent design for underwater warships. Studying the propagation of underwater shock wave in such structures is essential to comprehend their shock resistance. The aim of this paper is to investigate the propagation of underwater shock wave and water cavitation in a water-filled double plate. To achieve this objective, the paper establishes a Eulerian compressible fluid model that combines the isentropic single fluid model and Newton's second law. The accuracy of the numerical solver is confirmed through validation tests. The reflection and transmission characteristics of shock wave, the dynamic response of the plate, and the cavitation in external and gap water are analyzed. It also examines the effects of the supporting springs of outer and inner plates and the area density of the outer plate on the shock wave propagation and cavitation evolution. The findings indicate that the transmitted wave in the gap water is influenced by the area density and supporting spring of the outer plate. A thicker outer plate can reduce the peak value of the transmitted wave, and a stiffer supporting spring can decrease the transmitted impulse. On the other hand, if the outer plate is freestanding or softly supported, it has minimal effects on the response of the inner plate. Moreover, the water cavitation is determined by the supporting spring of the inner plate in the case of a softly supported outer plate, and the cavitation initially develops in the gap water near the inner plate before expanding towards the external water. When the supporting spring of the outer plate is stiff, it significantly reduces the occurrence of cavitation in the external water, while the cavitation in the gap water is still determined by the support spring of the inner plate. These research findings are valuable for analyzing the shock resistance of typical double-hull submarines.