Modelling of Lamb wave propagation in composite plate excited by surface bonded piezoelectrical actuators

Transient propagation of Lamb waves in a multilayered infinite composite plate with the arbitrary elastic anisotropy of each layer is considered in this paper. Integral representations of wave fields, an algorithm of computing the Green's matrix of the multilayered medium in Fourier domain and some methods of the Fourier transform inversion are used as basic analytical research instruments. The piezoelectrical transducers frequently used for Lamb wave excitation are modelled in this paper as surface sources with stresses concentrated on the boundaries of actuators. The contribution of each wave mode to a whole amplitude, focusing of Lamb waves and influence of the geometry of the surface source are discussed in this paper by numerical examples. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dispersion of lamb waves in a three-layer plate made from compressible materials with finite initial deformations

A three-layer plate made from compressible elastic materials with finite initial deformations caused by compressive forces applied to their faces is considered. By using the three-dimensional linearized theory of propagation of elastic waves in bodies with initial stresses, the propagation of Lamb waves in this plate is investigated.     

Three-dimensional analyses of stress singularities at the vertex of a piezoelectric wedge

The electroelastic singularities at the vertex of a rectilinearly polarized piezoelectric wedge are investigated using three-dimensional piezoelasticity theory. An eigenfunction expansion approach is combined with a power series solution technique to find the asymptotic solutions at the vertex of the wedge by directly solving the three-dimensional equilibrium and Maxwell’s equations in terms of the displacement components and electric potential. This study is the first to address the problems in which the polarization direction of the piezoelectric material is not necessarily either parallel to the normal of the mid-plane of wedge or in the mid-plane. The correctness of the proposed solution is verified by convergence studies and comparison with the published results that are based on generalized plan strain assumption. The solution is further employed to study comprehensively the effect of the direction of polarization on the electroelastic singularities of wedges that contain a single material (PZT-5H), bounded piezo/isotropic elastic materials (PZT-5H/Si), or piezo/piezo materials (PZT-5H/PZT-4).     

Effects of initial stress on guided waves in orthotropic functionally graded plates

Because of the limitation of the manufacturing technology, initial stress in functionally graded materials (FGM) and structures is inevitable. Based on the theory of “Mechanics of Incremental Deformations”, the guided wave propagation in FGM plates under gravity, homogeneous initial stress in the thickness direction and inhomogeneous initial stress in the wave propagation direction is investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. The convergence of the polynomial series method is discussed through the numerical examples. The effects of the initial stress on the Lamb-like wave and on the SH wave are investigated respectively and the numerical results show they are quite distinct. The effect of the gravity on the wave propagation can be ignored. The effects of the initial stress in the thickness direction are very different from those of the initial stress in the wave propagation direction, both on the dispersion curves and on the displacement and stress distributions.     

On the propagation of Lamb waves in a sandwich plate made of compressible materials with finite initial strains

The propagation of flexural Lamb waves in a prestrained sandwich plate made from compressible highly elastic materials is investigated within the scope of a piecewise homogeneous body model by utilizing TLTEWISB. The mechanical relations of layer materials are described by a harmonic-type potential, and numerical results are obtained for the first and second vibration modes. According to the results, the influence of problem parameters and of the initial stretching strain along the layers on the wave propagation speed is examined. The asymptotic values of the speed are considered in the cases of short and long wavelengths, and the influence of the initial strains on these asymptotic (limit) values are also analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 231–244, March–April, 2008.     

Reflection and transmission of elastic waves in the multilayered orthotropic couple-stressed plates sandwiched between two elastic half-spaces

In this paper, a high efficient computational approach, the extended Legendre orthogonal polynomial method (LOPM) is provided to investigate the reflection and transmission of elastic waves in orthotropic couple-stress layered plates sandwiched between two elastic half-spaces. In this approach, the anisotropic couple-stress theory is introduced into the LOPM to calculate the reflection and transmission coefficients of the orthotropic interlayers. The stress components, couple-stress components, rotation vectors and governing equations are derived in terms of the Legendre orthogonal polynomial. The present method does not require calculations of the displacement solutions of each partial wave in anisotropic multilayered microstructures, but expands the displacement vector of each layer into a Legendre orthogonal polynomial series with the expansion coefficients to be calculated. The incident P wave and SH wave are calculated, respectively. The effects of length scale parameters in three different directions are studied. It is found that the reflection and transmission coefficients of the incident P wave are only related to the length scale parameter in the z direction. For incident SH wave, the influence of the length scale parameter along the thickness direction is much more significant than that of the length scale parameter in the y direction.     

Investigation of Dispersion Characteristics of Composites

This numerical study of dispersion characteristics of some symmetric and asymmetric composites modelled as multilayered packets of layers with arbitrary anisotropy of each layer is carried out. The authors introduce a subsidiary boundary problem of three-dimensional theory of elasticity for the system of partial differential equations describing the harmonic oscillations of the composite excited by a surface load. The authors obtained the curves and surfaces describing slowness of the wave front of Lamb waves propagating with respect to the direction of propagation. The method suggested by the authors of the present article does not impose any restrictions on the type of elastic anisotropy of the layers, their orientations and mutual positions. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic analysis of wave fields when there is partial impulse delamination of the media

A method of solving transient wave problems with mixed boundary conditions for multilayered media [1–3] is generalized to problems in which the continuity breaks down. Unlike existing results [1, 4, 5], obtained for the case of the propagation of only harmonic perturbations from the initial instant of time, the space-time structure of the wave fields in the case of pulsed generation modes is investigated by an asymptotic analysis of the solution of a system of Wiener—Hopf type functional equations. The conditions for weak wave effects to arise for transient waves, due to the layered structure of semi-infinite media, are analysed.     

Green's function approach to study the propagation of SH‐wave in piezoelectric layer influenced by a point source

Green's function technique serves as a powerful tool to find the particle displacements due to SH‐wave propagation in layer of a shape different from the space between two parallel planes. Therefore, the present paper undertook to study the propagation of SH‐wave in a transversely isotropic piezoelectric layer under the influence of a point source and overlying a heterogeneous substrate using Green's function technique. The coupled electromechanical field equations are solved with the aid of Green's function technique. Expression for displacements in both layer and substrate, scalar potential and finally the dispersion relation is obtained analytically for the case when wave propagates along the direction of layering. Numerical computations are carried out and demonstrated with the aid of graphs for six different piezoelectric materials namely PZT‐5H ceramics, Barium titanate (BaTiO₃) ceramics, Silicon dioxide (SiO₂) glass, Borosilicate glass, Cobalt Iron Oxide (CoFe₂O₄), and Aluminum Nitride (AlN). The effects of heterogeneity, piezoelectric and dielectric constants on the dispersion curve are highlighted. Moreover, comparative study is carried out taking the phase velocity for different piezoelectric materials on one hand and isotropic case on the other. Dispersion relation is reduced to well‐known classical Love wave equation with a view to illuminate the authenticity of problem. Copyright © 2017 John Wiley & Sons, Ltd.     

Propagation of SH‐wave in an initially stressed orthotropic medium sandwiched by a homogeneous and an inhomogeneous semi‐infinite media

The paper presents a study of propagation of shear wave (SH‐wave) in an orthotropic elastic medium under initial stress sandwiched by a homogeneous semi‐infinite medium and an inhomogeneous half‐space. The technique of separation of variables has been adopted to get the analytical solutions for the dispersion relation in a closed form. The propagation of SH‐waves is influenced by inhomogeneity parameters and initial stress parameter. Velocities of SH‐waves are calculated numerically for different cases. As a special case when the intermediate layer and half‐space are homogeneous, computed frequency equation coincides with general equation of Love wave. To study the effect of inhomogeneity parameters and initial stress parameter, we have plotted the velocity of SH‐wave in several figures and observed that the velocity of wave decreases with the increases of non‐dimensional wave number. It can be found that the phase velocity decreases with the increase of inhomogeneity parameters. We observed that the velocity of SH‐wave decreases with the increases of initial stress parameter in both homogeneous and inhomogeneous media. GUI has been developed by using MATLAB to generalize the effect of the parameters discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

压电压磁复合材料中二维散射问题的解析研究

用极化方法分析了含一二维夹杂的无限压电压磁基体中的波动散射问题．以此为目的,首先构建了二维压电压磁“相对体”的极化方法．当一般性波动退减为简谐振动时,极化方法的核心函数退减为二维谐波Green函数．利用氡变换的解析方法,首次求得了二维谐波Green函数的积分表达式,该表达式在低频初始波与小尺度椭圆柱夹杂物的假设下可得到进一步的简化,并最终求得解析解．推导针对同时具有压电以及压磁效应的一般性各向异性材料进行,然后将所得的结果简化到仅针对压电复合材料的情况．以此简化解析解为基础,提供了两个算例,讨论了影响含一二维椭圆柱夹杂的PZT-5H压电陶瓷复合材料的散射截面的各种不同因素（包括夹杂的尺寸、形状效应,材料常数的影响,以及压电效应等）．     

On Love-type waves in a finitely deformed magnetoelastic layered half-space

In this paper, the propagation of Love-type waves in a homogeneously and finitely deformed layered half-space of an incompressible non-conducting magnetoelastic material in the presence of an initial uniform magnetic field is analyzed. The equations and boundary conditions governing linearized incremental motions superimposed on an underlying deformation and magnetic field for a magnetoelastic material are summarized and then specialized to a form appropriate for the study of Love-type waves in a layered half-space. The wave propagation problem is then analyzed for different directions of the initial magnetic field for two different magnetoelastic energy functions, which are generalizations of the standard neo-Hookean and Mooney?CRivlin elasticity models. The resulting wave speed characteristics in general depend significantly on the initial magnetic field as well as on the initial finite deformation, and the results are illustrated graphically for different combinations of these parameters. In the absence of a layer, shear horizontal surface waves do not exist in a purely elastic material, but the presence of a magnetic field normal to the sagittal plane makes such waves possible, these being analogous to Bleustein?CGulyaev waves in piezoelectric materials. Such waves are discussed briefly at the end of the paper.     

Estimation of interface damage of fiber-reinforced composites

The estimation of interface damage of fiber-reinforced composites based on the propagation constants of coherent waves is studied in this paper. First, the relation between the interface damage and the propagation constants is investigated by using the theory of multiple scattering. Next, single and multiple scatterings in the composites in the case of incident P, SV, and SH waves are considered. The propagation constants of coherent waves are computed numerically, and the influence of interface damage on them is discussed. Then, based on the relation between the propagation constants and the interface damage, an inverse method to estimate the interface damage is proposed. Finally, a numerical example is given. The numerical results are obtained by using synthetic experimental data and the genetic algorithm. It is shown by the numerical example that the interface damage can be approximately estimated from the wave propagation constants measured with various degrees of accuracy.     

The propagation of elastic waves in composite materials reinforced with piezoelectric fibres

The propagation of longitudinal elastic waves in composite materials, consisting of a polymer matrix reinforced by continuous fibres in one direction, is considered. The reinforcing fibres have piezoelectric properties and have a thin current-conducting coating (“shunted fibres”). The scattering of electric energy in such materials leads to dispersion of the velocity of the elastic waves and to their attenuation. The effective-field method is used to determine the macroscopic electroelastic constants of such composites. These constants enable one to obtain, in explicit form, the frequency dependence of the real and imaginary parts of the wave number of a longitudinal wave, propagating along the reinforcement direction, and also their dependenc on the physical and geometrical characteristics of the components.     

Propagation of shear waves in piezoelectric “superlattice-substrate” structures

The results of a computer simulation of the dispersion relations for the propagation of shear waves in piezoelectric “superlattice-substrate” structures are analyzed. The superlattice consists of a finite number of layers and is made up of materials with 6mm symmetry. The dispersion relations are obtained using a formulation for periodic hamiltonian systems. This approach makes it possible to account for the anisotropy, the piezoelectric interaction of the mechanical and electric fields, and an arbitrary number of layers in the superlattice. Numerical results are presented for CdS-ZnO layers. Selective spatial localization of acoustic modes is demonstrated for different spectral regions. The effects of the ordering of the superlattice layers, of their number, and of the boundary conditions on the dispersion spectra and on the form of the shear wave motion are examined. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, and Institute of Metal Physics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 148–156, 1999.     

A generalized dynamic model of nanoscale surface acoustic wave sensors and its applications in Love wave propagation and shear-horizontal vibration

A generalized dynamic model to depict the wave propagation properties in surface acoustic wave nano-devices is established based on the Hamilton's principle and variational approach. The surface effect, equivalent to additional thin films, is included with the aid of the surface elasticity, surface piezoelectricity and surface permittivity. It is demonstrated that this generalized dynamic model can be reduced into some classical cases, suitable for macro-scale and nano-scale, if some specific assumptions are utilized. In numerical simulations, Love wave propagation in a typical surface acoustic wave device composed of a piezoelectric ceramic transducer film and an aluminum substrate, as well as the shear-horizontal vibration of a piezoelectric plate, is investigated consequently to qualitatively and quantitatively analyze the surface effect. Correspondingly, a critical thickness that distinguishes surface effect from macro-mechanical behaviors is proposed, below which the size-dependent properties must be considered. Not limited as Love waves, the theoretical model will provide us a useful mathematical tool to analyze surface effect in nano-devices, which can be easily extended to other type of waves, such as Bleustein-Gulyaev waves and general Rayleigh waves.     

Damage detection in plates by wave propagation analyses

At locations with defects the propagation of elastic waves in solids is disturbed. This behaviour can be used for the development of new structural health monitoring and quality assurance systems. In the sense of adaptive structure systems actuators of piezo–electric materials [1] are implemented to generate high frequency waves (Lamb waves) in plate like structures, [2]. At flaws, imperfections of the structure and surface defects these waves show reflections, refractions and mode conversions. The observation of the wave propagation and the wave behaviour at possible flaws and surface defects is performed by an optical measurement system. Measurement data of the thin walled metallic plates are compared with numerical and analytical solutions. First results of the detection of the wave propagation in metallic plates are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Piezoelectric Induced Lamb Waves in Plates

In the paper, piezoelectric induced Lamb wave propagation on homogeneous plates is studied by applying different approaches. Assuming the presence of piezoelectric actuators and sensors the transient wave analysis is made using the classical formulation of the finite element method (FEM) and the novel approach of spectral finite element method (SE). Pure mode excitation and mode conversion are numerically simulated for the fundamental modes S₀ and A₀. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

BELENE nuclear power plant numerical and experimental bedrock,layers and surface signals

An investigation of BELENE Nuclear Power Plant (NPP) free field signal is presented in the current study. An SH wave propagation trough multilayer geological media in the region is considered. An original structural model of the geological column has been developed. The investigated layers are isotropic, with constant depth and skyline parallel. The SH rays are with an arbitrary angle as far as the layers are concerned. The seismic SH waves have been generated by a special detonation device. The main results of the study are graphically illustrated. A comparison between the original BELENE NPP experimental and the numerical surface (free field) signals (obtained by the formulated direct problem) for the investigated geological column has been carried out and its results are hereby shown.     

Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space

In the present paper, the dispersion equation which determines the velocity of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space has been obtained. The dispersion equation obtained is in agreement with the classical result of Love wave when the initial stresses and inhomogeneity parameters are neglected. Numerical results analyzing the dispersion equation are discussed and presented graphically. The result shows that the initial stresses have a pronounced influence on the propagation of torsional surface waves. It has also been shown that the effect of density, directional rigidities and non-homogeneity parameter on the propagation of torsional surface waves is prominent.