Transference of SH waves through irregular interface between corrugated piezoelectric layer and prestressed viscoelastic substrate

An exact approach is used to investigate the horizontally polarized shear wave in an irregular piezoelectric layer with corrugated surface lying over prestressed viscoelastic substrate. Perturbation technique is used to solve the problem. Dispersion relations are obtained in closed form for electrically open and short cases. The main feature of the present work is its ability to investigate the effect of irregularity, corrugation, dielectric constant, piezoelectric constant, initial stress and viscoelastic parameter on the phase velocity of SH wave. Numerical example has been carried out to observe the profound effect of these affecting parameters on phase velocity of SH wave.     

Love waves in a smart functionally graded piezoelectric composite structure

The propagation of Love waves in a smart functionally graded piezoelectric structure is analyzed by applying elastic wave theory. There is an additional functionally graded layer between the piezoelectric layer and the substrate in this smart structure. When the piezoelectric and dielectric constants vary individually in a functionally graded layer, the asymptotic solutions of Love waves are obtained by applying the WKB method and solving the fourth order differential equation with variable coefficients. The effects of gradient variation on the phase velocity and the coupled electromechanical factor are discussed in detail. The analysis shows that the number of vibration modes is greater than that in the non-graded layer structure, and the coupled electromechanical factor increases with the increase of piezoelectric constant graded variation. Presented results are useful for the improvement of properties of surface acoustic wave (SAW) devices.     

Efficient coupled refined finite element for dynamic analysis of sandwich beams containing embedded shear-mode piezoelectric layers

An efficient and computationally low cost finite element (FE) model is developed for dynamic free and forced response of sandwich beams with embedded shear piezoelectric layers based on a coupled refined high-order global-local theory. Contrary to most of the available models, all of the kinematic and stress boundary conditions are ensured at the interfaces of the shear piezoelectric layers. Moreover, both the electrical-induced strains components and transverse flexibility are taken into account for the first time in the present theory. For validation of the proposed model, various free and forced vibration tests for thin and thick sandwich beams are carried out. For various electrical and mechanical boundary conditions, excellent agreement has been found between the results obtained from the proposed formulation with previously published and the coupled two-dimensional (2D) FE results.     

Dispersion and characteristic surfaces of waves in hybrid multilayered piezoelectric circular cylinders

The frequency and group velocity dispersion behaviors, and characteristic surfaces of waves in a hybrid multilayered piezoelectric circular cylinder are investigated. The associated frequency dispersion equation is developed using an analytical-numerical method. In this method, the cylinder is modeled using the three-nodal-line layer element; the coupling between the elastic field and the electric field is considered in each element. A system of governing differential equations of each layer element is obtained following the Hamilton Principle. The phase velocity and slowness as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces, e.g. the phase velocity, slowness and wave surfaces as well as the group velocity, slowness and wave surfaces, are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. A corresponding program code is developed and numerical examples are presented for hybrid multilayered piezoelectric circular cylinders with two ratios of radius to thickness.     

Love waves propagation in a piezoelectric layered structure with initial stresses

Summary. The propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress is studied. Solutions of the mechanical displacement and electrical potential function are obtained for the isotropic elastic layer and transversely isotropic piezoelectric substrate, respectively, by solving the coupled electromechanical field equations. Firstly, effects of the inhomogeneous initial stress on the dispersion relations and phase velocity of Love wave propagation are discussed. Then the influence of the initial stress gradient coefficient on the stress, mechanical displacement and electrical potential distribution in the layer and the substrate is investigated in detail. The results reported in this paper are not only meaningful for the design of surface acoustic wave (SAW) devices with high performance, but also effective for evaluating the residual stress distribution in the layered structures.     

Shear-horizontal piezoelectric waves in an aluminum nitride film on a silicon substrate

The propagation of shear-horizontal waves in a piezoelectric film of aluminum nitride on a silicon substrate is studied. Three different electrode configurations are considered for thin film acoustic wave resonator application. A theoretical analysis is performed. The equations of linear piezoelectricity and anisotropic elasticity are used for the film and the substrate, respectively. Real and imaginary dispersion curves as well as electromechanical mode shapes are obtained. The effects of electrode configuration on the distribution of the electromechanical fields and the dispersion curves of long thickness-twist waves as well as energy trapping are examined.     

Simulation of piezoelectric excitation of guided waves using waveguide finite elements

A numerical method for computing the time response of infinite constant cross-section elastic waveguides excited by piezoelectric transducers was developed. The method combined waveguide finite elements (semi-analytical finite elements) for modeling the waveguide with conventional 3-D piezoelectric finite elements for modeling the transducer. The frequency response of the coupled system was computed and then used to simulate the time response to tone-burst electrical excitation. A technique for identifying and separating the propagating modes was devised, which enabled the computation of the response of a selected reduced number of modes. The method was applied to a rail excited by a piezoelectric patch transducer, and excellent agreement with measured responses was obtained. It was found that it is necessary to include damping in the waveguide model if the response near a "cut-on" frequency is to be simulated in the near-field.     

Scattering of antiplane shear waves by a finite crack in piezoelectric laminates

Summary Following the dynamic theory of linear piezoelectricity, we consider the scattering of horizontally polarized shear waves by a finite crack in a composite laminate containing a piezoelectric layer. The piezoelectric layer is bonded between two half-spaces of a different elastic solid. The crack is normal to the interfaces and is placed at an equal distance away from them. Both cases of a partially broken layer and a completely broken layer are studied. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a singular integral equation. The propagation of symmetric first mode is studied numerically, and the dynamic stress intensity factor and the dynamic energy release rate are obtained for some piezoelectric laminates.     

功能梯度压电层/压电半空间结构中Love波的传播:一种改进的拉盖尔多项式方法

使用传统的拉盖尔多项式方法求解层状半空间结构时,存在因层间材料差异所造成的应力、电位移不连续的现象。为了克服此方法的不足,提出了一种改进的拉盖尔多项式方法,研究了功能梯度压电层状半空间中Love波的传播特性。与文献中应用WKB法得到的结果进行对比,验证了该方法的正确性。计算和分析了相应的频散曲线、应力和电位移分布曲线。结果表明:该方法能够避免因层间材料差异所造成的应力、电位移不连续现象的出现;高频Love波的应力和电位移主要分布在功能梯度压电层中速度较低的一侧。该研究为基于Love波传感器的设计与优化奠定了一定的理论基础。     

Propagation of low-frequency elastic waves in double-porositymedia containing viscoelastic component in the pores

A self-consistent scheme named the effective field method (EFM) is applied for the calculation of the velocities and quality factors of elastic waves propagating in double-porosity media. A double-porosity medium is considered to be a heterogeneous material composed of a matrix with primary pores and inclusions that are represent by flat (crack-like) secondary pores. The prediction of the effective viscoelastic moduli consists of two steps. First, we calculate the effective viscoelastic properties of the matrix with the primary small-scale pores (matrix homogenization). Then, the porous matrix is treated as a homogeneous isotropic host where the large-scale secondary pores are embedded. Spatial distribution of inclusions in the medium is taken into account via a special two-point correlation function. The results of the calculation of the viscoelastic properties of double-porosity media containing isotropic fields of crack-like inclusions and double-porosity media with some non-isotropic spatial distributions of crack-like inclusions are presented.     

Sensitivity analysis of frequency response functions of composite sandwich plates containing viscoelastic layers

In the scope of structural dynamics, sensitivity analysis is a very useful tool in a number of numerical procedures such as parameter identification, model updating, optimal design and uncertainty propagation. In this paper the formulation of first-order sensitivity analysis of complex frequency response functions (FRFs) is developed for composite sandwich plates composed by a combination of fiber-reinforced and elastomeric viscoelastic layers, in arrangements that are frequently used for the purpose of noise and vibration attenuation. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to viscoelastic structures, which are characterized by frequency- and temperature-dependent material properties and, thus, require particularly adapted analytical and numerical procedures. Due to the fact that finite element discretization has become the most used method for dynamic analysis of complex structures, the sensitivity analysis addressed herein is based on such models, being computed from the analytical derivatives of the FRFs with respect to a set of design parameters, such as fiber orientations and layer thicknesses. Also, a procedure for evaluating the sensitivity of the FRFs with respect to temperature of the viscoelastic material is suggested. After discussion of various theoretical aspects, including a parameterization scheme of the structural matrices with respect to the design variables, first-order response derivatives are calculated for a composite plate with inherent structural damping, and for a composite sandwich plate with a viscoelastic core. The results are compared to those obtained from first-order finite-difference approximations.     

Analysis of an orthotropic strip containing multiple defects bonded between two piezoelectric layers

In this paper, the problem of multiple defects in an orthotropic layer bonded between two piezoelectric layers is considered. The analysis is based on the stress fields caused by Volterra-type screw dislocation in the orthotropic strip. The solution for the dislocation is obtained by means of the complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple defects. These equations, as a class of Cauchy singular equations, are solved numerically for dislocation density functions. A number of examples is given for various crack orientations and material properties. At the end, it is shown that the effect of the properties and defect geometries on the stress intensity factors and hoop stress for cavities can be highly significant.     

Characteristic parameters of surface acoustic waves in a periodic metal grating on a piezoelectric substrate

The coupling problem between electrodes due to the propagation of acoustic waves in a periodic metal grating on a piezoelectric substrate is theoretically studied. A method for the determination of the mutual admittance between the grating electrodes is presented, and an analytical expression for the contribution of surface acoustic waves (SAWs) is proposed. The SAW characteristic parameters are determined with a numerical technique that is able to deal with a leaky SAW as well as a true SAW (conventional Rayleigh type or Bleustein-Gulyaev type). Using this technique, the SAWs' contribution to the mutual admittance can be removed, and the analysis of other contributions becomes possible. In particular, the amplitude decay rate of the residual mutual admittance with electrode separation gives information about the propagation of the surface skimming bulk waves (SSBWs). The method presented is applied to several currently used material-cut configurations.     

Love waves on a half-space with a gradient piezoelectric layer by the geometric integration method

The propagation of Love waves on an elastic homogeneous half-space with a piezoelectric gradient covering layer is studied by the geometric integration method in this article. First, the state transfer equation of a Love wave is derived from the governing equations and constitutive relations. Then, the transfer matrix of the state vector is obtained by solving the state transfer equation of a Love wave and then the stiffness matrix is obtained. By combining transfer matrices and the stiffness matrices of the gradient covering layer and the homogeneous half-space, the total surface stiffness matrix of a Love wave is obtained. Lastly, the application of the electrically open circuit and short circuit conditions and mechanically traction-free conditions gives the frequency dispersive relation of a Love wave. For the gradient covering layer, the material constants at the bottom of the covering layer may be greater or smaller than that at the top of the covering layer. The two situations and three kinds of gradient profiles for each of these two situations are investigated. The numerical results show that the Love wave speed is sensitive to not only the material constants at the bottom and the top of the covering layer, but also the gradient profiles of the covering layer.     

Transverse surface waves in a piezoelectric material carrying a gradient metal layer of finite thickness

The existence and propagation behavior of transverse surface waves in a layered structure concerning a piezoelectric substrate and a gradient metal layer are theoretically investigated in this paper. The Wentzel-Kramers-Brillouin (WKB) method is applied to obtain the analytical solutions in the gradient metal layer. The dispersion equation for transverse surface waves in such structure is obtained in a quite simple mathematical form, where the material gradient of the metal layer assumes arbitrary functions. Effects of material gradient on three types of dispersion behavior are discussed in detail based on a proper classification. Numerical results show that the material gradient in the metal layer evidently affects the fundamental mode shape of the transverse surface waves but has negligible effects on the higher order modes.     

Full-wave analysis of piezoelectric boundary waves propagating along metallic grating sandwiched between two semi-infinite layers

This paper describes full-wave analysis of piezoelectric boundary acoustic waves (PBAWs) propagating along a metallic grating sandwiched between 2 semi-infinite layers. In the analysis, the finite element method (FEM) is used for the grating region while the spectral domain analysis (SDA) is applied for an isotropic overlay region as well as a piezoelectric substrate region. The combination of the FEM and SDA makes the numerical analysis very fast and precise. As an example, the analysis was made on the PBAWs propagating in an SiO₂ overlay/ Cu grating/rotated Y-cut LiNbO₃ structure. It is shown that both the shear-horizontal (SH) type and Rayleigh-type PBAWs are supported in the structure, and that their velocities are very close to each other. Thus spurious responses due to the Rayleigh-type PBAW should completely be suppressed for device implementation. Discussions are made in detail on the influence of Cu grating thickness, substrate rotation angle, and metallization ratio on excitation and propagation characteristics of the SH- and Rayleigh-type PBAWs.     

Band gaps of lamb waves in one- dimensional piezoelectric composite plates: effect of substrate and boundary conditions

We theoretically study the band structures of Lamb waves in one-dimensional phononic crystal plates consisting of piezoelectric ceramics placed periodically in epoxy with epoxy or piezoelectric ceramic substrate by the virtual plane wave expansion method. The dependences of the widths and starting frequencies of first band gaps (FBG) on the substrate's thickness, the filling fraction, and the lattice spacing are calculated for different materials of substrate under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). The FBG width decreases gradually as the substrate's thickness increases and the FBG starting frequency increases progressively as the thickness increases on the whole. The FBG widths and starting frequencies with SC are always larger than with OC. Our research shows that it is possible to control the width and starting frequency of the FBG in the engineering according to need by choosing suitable values of the substrate?s thickness, the filling fraction, and the lattice spacing.     

Propagation of shear waves generated by a modulated finite amplitude radiation force in a viscoelastic medium

An effective way to generate localized narrow-band low-frequency shear waves within tissue noninvasively, is by the modulated radiation force, resulting from the interference of two confocal quasi-CW ultrasound beams of slightly different frequencies. By using approximate viscoelastic Green's functions, investigations of the properties of the propagated shear-field component at the fundamental modulation frequency were previously reported by our group. However, high-amplitude source excitations may be needed to increase the signal-to-noise-ratio for shear-wave detection in tissue. This paper reports a study of the generation and propagation of dynamic radiation force components at harmonics of the modulation frequency for conditions that generally correspond to diagnostic safety standards. We describe the propagation characteristics of the resulting harmonic shear waves and discuss how they depend on the parameters of nonlinearity, focusing gain, and absorption. For conditions of high viscosity (believed to be characteristic of soft tissue) and higher modulation frequencies, the approximate shear wave Green's function is inappropriate. A more exact viscoelastic Green's function is derived in k-space, and using this, it is shown that the lowpass and dispersive effects, associated with a Voigt model of tissue, are more accurately represented. Finally, it is shown how the viscoelastic properties of the propagating medium can be estimated, based on several spectral components of the shear wave spectrum.     

Shock waves in random viscoelastic media

Determining the effects of material spatial randomness on the evolution of shocks is the objective of this study. Considering a linear viscoelastic-type material, a very general class of random media is modeled by a three-component random vector field: the instantaneous relaxation function (E), its derivative (E′), and the mass density (ρ). The reason for considering the randomness of the said material coefficients is the fact that a wavefront’s length scale (thickness) is most likely smaller than the Representative Volume Element, thus contradicting a “separation of scales” condition tacitly assumed in deterministic continuum mechanics, even in the context of wavefront analyses. In effect, the wavefront is an object much more appropriately analyzed as a Statistical Volume Element and therefore to be treated via a stochastic dynamical system rather than a deterministic one. Various cases of the random vector field [E, E′, ρ] _x are examined: white versus correlated noises as well as the independence versus coupling of these random fields to the shock amplitude.