Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.     

The dispersion of shear wave in multilayered magnetoelastic self-reinforced media

In this paper, we study the propagation of shear waves in a magnetoelastic self-reinforced medium using finite difference technique. Dispersion equation has been deduced for the case when (n ? 1) layers lie over a half space. It is observed that the obtained dispersion equation is in assertion with the classical Love wave equation for both the cases when a single and double layer lies over a half space. The stability condition for the used finite difference scheme and the expression for the phase and group velocity have been derived. The dispersion curve for different values of magnetoelastic coupling parameter, phase and group velocity variation for different values of stability ratio has been depicted by means of graphs.     

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and a dielectric layer

The existence and behaviour of electro-elastic surface Love waves in a structure consisting of a piezoelectric substrate of crystal classe 6, 4, 6 mm, 4 mm, 622 or 422, an elastic layer and a dielectric medium is considered. The mathematical model obtained includes all the above crystal classes, i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The dispersion equation for the existence of Love surface waves with respect to phase velocity is obtained. A detailed investigation of the electromechanical coupling coefficient is carried out depending on the dielectric and piezoelectric parameters of the problem. Geometrical investigation of the solutions of the dispersion equation is carried out.     

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and two isotropic layers

Propagation of electro-elastic surface Love waves in a structure consisting of a piezoelectric half-space substrate of crystal class 6, 4, 6 mm or 4 mm and two layers, one of which (adjacent to the substrate) is a conducting material and the second is either a conducting or a dielectric material, is considered. The mathematical model obtained includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The dispersion equation for the existence of Love surface waves with respect to phase velocity is obtained. Numerical calculations are carried out for three different layered structures. The effect of the second layer on the propagation behaviour of the surface Love wave in the structure is revealed.     

Propagation and localization of two-dimensional in-plane elastic waves in randomly disordered layered piezoelectric phononic crystals

Two-dimensional in-plane wave propagation and localization in the disordered layered piezoelectric phononic crystals with material 6 mm are investigated taking the electromechanical coupling into account. The electric field is approximated as quasi-static. The analytical solutions of elastic waves are obtained. The 6 × 6 transfer matrix between two consecutive unit cells is obtained by means of the mechanical and electrical continuity conditions. The expressions of the localization factor and localization length in the disordered periodic structures are presented by regarding the variables of the mechanical and electrical fields as the elements of the state vector. The numerical results of the localization factors and localization lengths are presented for two kinds of disordered piezoelectric phononic crystals, i.e. ZnO–PZT–5H and PVDF–PZT–5H piezocomposites. It is seen from the results that the incident angle of elastic waves and the thickness of the piezoelectric ceramics have significant effects on the wave localization characteristics. For different piezoelectric phononic crystals, the effects of the incident angle are very different. Moreover, with the increase of the disorder degree, the localization phenomenon is strengthened.     

Propagation of Bleustein–Gulyaev wave in 6 mm piezoelectric materials loaded with viscous liquid

The influence of a viscous liquid on acoustic waves propagating in elastic or piezoelectric materials is of particular significance for development of liquid sensors. Bleustein–Gulyaev wave is a shear-type surface acoustic wave and has the advantage of not radiating energy into the adjacent liquid. These features make the B–G wave sensitive to changes in both mechanical and electrical properties of the surrounding environment. The Bleustein–Gulyaev wave has been reported to be a good candidate for liquid sensing application. In this paper, we investigate the potential application of B–G wave in 6 mm crystals for liquid sensing. The explicit dispersion relations for both open circuit and metalized surface boundary conditions are given. A numerical example of PZT-5H piezoelectric ceramic in contact with viscous liquid is calculated and discussed. Numerical results of attenuation and phase velocity versus viscosity, density of the liquid and wave frequency are presented. The paper is intended to provide essential data for liquid senor design and development.     

Propagation behavior of Love waves in a functionally graded half-space with initial stress

The propagation behavior of Love waves in a functionally graded material layered non-piezoelectric half-space with initial stress is taken into account. The Wentzel–Kramers–Brillouin (WKB) technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of the mechanical displacement and stress along the thickness direction in the layered structure. First, these solutions are used to study the effects of the initial stress on the dispersion relations and the group and phase velocities, then the influences of the initial stress on the distributions of the mechanical displacement and shear stresses along the thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of the Love waves increases with the increase in the magnitude of the initial tensile stress, while decreases with the increase in the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100 MPa. Some other results are obtained for the distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.     

Critical velocity of sandwich cylindrical shell under moving internal pressure

Critical velocity of an infinite long sandwich shell under moving internal pressure is studied using the sandwich shell theory and elastodynamics theory. Propagation of axisymmetric free harmonic waves in the sandwich shell is studied using the sandwich shell theory by considering compressibility and transverse shear deformation of the core, and transverse shear deformation of face sheets. Based on the elastodynamics theory, displacement components expanded by Legendre polynomials, and position-dependent elastic constants and densities are introduced into the equations of motion. Critical velocity is the minimum phase velocity on the desperation relation curve obtained by using the two methods. Numerical examples and the finite element （FE） simulations are presented. The results show that the two critical velocities agree well with each other, and two desperation relation curves agree well with each other when the wave number k is relatively small. However, two limit phase velocities approach to the shear wave velocities of the face sheet and the core respectively when k limits to infinite. The two methods are efficient in the investigation of wave propagation in a sandwich cylindrical shell when k is relatively small. The critical velocity predicted in the FE simulations agrees with theoretical prediction.     

Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer

This paper presents the wave propagation in a cylinder coated with a thin piezoelectric layer. The piezoelectric coupling effects are fully modeled in the mechanics model for this piezoelectric coupled cylindrical shell with bending resistance. The decoupled torsional wave velocity and the dispersion curves for the two- mode shell model are obtained theoretically. The cut-off frequency and phase velocities at limit wave number are also derived. The numerical simulations are conducted to present the results of wave propagation in this cylindrical shell and as well as to compare the results by the current bending theory and the membrane shell theory. From the comparisons, the results display obvious deference of wave propagations in terms of dispersion characteristics by different shell theories when thicker piezoelectric layer are used and when higher wave number is considered. The results of this paper can serve as a reference for future study on wave propagation in coupled structures as well as in the design of smart structures incorporating piezoelectric materials.     

Inhomogeneous wave propagation in partially saturated soils

In the present study, inhomogeneous plane harmonic waves propagation in dissipative partially saturated soils are investigated. The analytical model for the dissipative partially saturated soils is solved in terms of Christoffel equations. These Christoffel equations yields the existence of four wave (three longitudinal and one shear) modes in partially saturated soils. Christoffel equations are further solved to determine the complex velocities and polarizations of four wave modes. Inhomogeneous propagation is considered through a particular specification of complex slowness vector. A finite non-dimensional inhomogeneity parameter is considered to represent the inhomogeneous nature of these four waves. Impact of tortuosity parameter on the movement of pore fluids is considered. Hence, the considered model is capable of describing the wave behavior at high as well as mid and low frequencies. Numerical example is considered to study the effects of inhomogeneity parameter, saturation of water, porosity, permeability, viscosity of fluid phase and wave frequency on the velocity and attenuation of four waves. It is observed that all the waves are dispersive in nature (i.e., frequency dependent).     

Mechanism of shear attenuation near the interface under combined compression and shear impact loading

We investigate the compressional/shear coupling plastic wave propagation characteristics analytically for ideal elastic–plastic materials in both stress and particle velocity spaces, focusing on the shear wave attenuation near the interface occurring in pressure–shear plate impact experiments. The results show that the shear attenuation is strongly associated with the wave propagation characteristics of the coupling waves. In the stress space, as the shear stress increases, an adjustment of the stress components is observed and the final stress state along the wave path is a combined pure shear- and hydrostatic pressure-state. In the particle velocity space, the wave structures with different loading and maximal transverse particle velocity are obtained. The maximal transverse particle velocity varies with the longitudinal velocity and forms a boundary line. Once the loading transverse velocity exceeds this line, a transverse particle velocity discontinuity occurs at the impact interface. If the bonding strength is sufficiently high, there will be a shear band in the target in the extreme vicinity of the interface.     

Reflection and Transmission of Elastic Waves at the Interface Between Water and a Double Porosity Solid

The reflection and transmission of an incident plane wave at an interface between water and a fluid-saturated double porosity solid are investigated. The properties of the three compressional waves and one shear wave in double porosity media are discussed in detail. The effect of the viscosity, permeability, and porosity on the phase velocity and attenuation of four bulk waves is presented. Comparison between the double porosity theory and the Biot theory reveals that there exists obvious difference in the phase velocity, attenuation and the reflection and transmission coefficients. Two cases of boundary conditions, i.e., the sealed-pore and the open-pore boundaries, are introduced in the numerical calculation. At last, the effect of the fracture permeability and porosity on the reflection and transmission coefficients considered. It is revealed that the amplitudes of the reflected and transmitted waves strongly depend the boundary condition, fracture permeability, and porosity.     

SH Waves in(1-x)Pb(Mg_(1/3)Nb_(2/3))O_(3-x)PbTiO_3 Piezoelectric Layered Structures Loaded with Viscous Liquid

The velocity dispersion and attenuation of shear horizontal(SH) waves in a layered piezoelectric structure loaded with viscous liquid is studied,where the(1- x)Pb(Mg_(1/3)Nb_(2/3))O_(3-x)PbTiO_3[PMN-xPT]single crystal is chosen as the piezoelectric layer.The PMN-xPT is being polarized along[011]_c and[001]_c so that the macroscopic symmetries are mm 2 and 4 mm,respectively.For the nonconductive liquid,the electrically open and shorted conditions at the interface between the liquid and the piezoelectric layer are considered.The phase velocity equations are derived analytically.The effects of the electrically boundary condition,the viscous coefficient and mass density of liquid as well as the thickness of the PMN-xPT layer on the phase velocity and attenuation are graphically illustrated.The results show that the phase velocity for the[011]_c polarized PMN-0.29 PT is much smaller than that for the[001]_c polarized PMN-0.33 PT,and the effects of viscous coefficient and piezoelectric layer thickness on the phase velocity for the[011]_c case are stronger than that for the[001]_c case.In addition,the electrical boundary conditions have an obvious influence on the propagation behaviors.These results can be useful for the designs and applications of acoustic wave devices and liquid biosensors.     

初应力对压电层状结构声表面波传播性能的影响

研究了压电层状结构中初应力对广义Ｒａｙｌｅｉｇｈ波传播相速度和机电耦合性能的影响,通过求解含初应力的运动微分方程,对自由界面电学开路和短路两种情况得到了相应的相速度方程。给出了具体的数值算例,所得结果对于提高和改善声表面波器件性能有参考意义。     

基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。     

Effects of covering layer thickness on Love waves in functionally graded piezoelectric substrates

An analytical approach is used to investigate the effects of covering layer thickness on the propagation behavior of Love waves in functionally graded piezoelectric materials (FGPMs) covered with a dielectric layer. The piezoelectric substrate is polarized in the direction perpendicular to the wave propagation plane, and its material parameters change continuously along the thickness direction. The dispersion equations for the existence of Love waves with respect to phase velocity are obtained for electrically open and shorted cases, respectively. A detailed investigation of the effects of the covering dielectric layer thickness on dispersion curve, phase velocity, group velocity, and electromechanical coupling factor is carried out. Numerical results show that for a given FGPM, the covering dielectric layer thickness affects significantly the fundamental mode of Love waves but has only negligible effects on the high-order modes. The changes in phase velocity, group velocity, and electromechanical coupling factor due to the change of gradient coefficient of FGPMs could be approached approximately by changing the thickness of the covering dielectric layer, which imply a potential factor for designing new-type surface wave devices with FGPMs.     

Wave propagation in a piezoelectric rod of 6 mm symmetry

The wave propagation in a piezoelectric rod of 6 mm symmetry is investigated by applying a 3-D piezoelectric elastic model. A self-adjoint method is introduced to solve this problem, this method avoids calculating the generalized eigenvalue equation, it completely draws the dispersion curves in the forms of Quasi-P wave, Quasi-SV wave and Quasi-SH wave under the self-adjoint boundary condition, and it can evaluate the dispersion curves of all kinds of boundary conditions. As an example, the dispersion curves of PLT-5H are completely drawn, we also found the Quasi-SV wave has standing wave phenomenon in the PLT-5H rod. In addition the relation of dispersion curves among different boundary conditions is discussed, and an experiment method is introduce to decide the dispersion curves for another boundary conditions.     

Plane Horizontal Transverse Waves in Elastic Piezopowders

A procedure and results of computer simulation of plane horizontal transverse waves are described. Three materials — gallium arsenide, bismuth germanate, and lead zirconate–titanate ceramics — are selected as the piezoelectric phase. The second phase of the powder is always lead. To describe waves in the powder, the microstructural theory of two-phase mixtures is used. Therefore, the computer simulation was intended to study the influence of the lead content by volume on the wave velocities and the microstructural wave-propagation pattern — decomposition of a wave into two modes, simultaneous propagation of both modes in each phase of the powder, etc. First, sets of physical constants (elastic, piezoelectric, and dielectric) of mixture theory were evaluated for three types of powders (with the piezoelectric phase as one of the above-mentioned materials) with the volume piezoelectric-phase content varying from 0.01 to 0.5 with step 0.005. Further, dispersion curves for both modes and 3D-graphs of amplitudes as functions of the wave propagation time and distance were plotted for 300 compositions of powders (three types, each of 100 modifications). Of the phenomena described, we should first of all point out that all the phase velocities increase twice upon changing the content of the powder in the piezoelectric phase from a very small amount to the maximum possible     

Dual-element directional shock wave attenuators

This study explores the interaction between shock waves and dual-element porous plates used to ameliorate the hazardous effects of these waves. Tests were performed in a shock tube to determine the effects that a pair of porous plates with directional resistance properties had on the initial peak pressure and impulse amelioration experienced by an end wall. Mild steel test specimens, ranging in porosity values from 6.6% to 41.1%, were mounted two at a time at different spacings in the test section. Each plate had directional properties, i.e. resistance to flow was different for flow coming from either side. Four plates were used, and 48 plate configurations were tested. Side wall and end wall pressure measurements and schlieren photographs were taken of the interactions. Tests were run at Mach numbers of 1.23, 1.35 and 1.42. The separation distances between the plate specimens were varied between 30 mm and 60 mm; however, the distance between the downstream plate and the end wall was kept constant at 140 mm for all tests.Both the initial peak pressure and impulse amelioration values were found to be dependant on the plate combination porosity. As the porosity of the combination increased, the amelioration values decreased. Complementary plate combinations produced differing results as different wave interactions occur when plate positions were interchanged. The porosity of the combined plates was found to have an overriding influence on the end wall peak pressure and impulse amelioration values when compared to the effect that plate arrangement (i.e. geometrical influences) had. Impulse amelioration values were found to increase as the separation distance between plates were increased. The amplitude of the end wall pressure trace was found to increase as the incident Mach number was increased. The significant attenuation of the incident shock wave obtained during this study is attributed to the system of multiple reflected and transmitted waves that are produced by the presence of the plate specimens in series. This increases the frequency of shock wave and barrier interactions, when compared to just using a single barrier.     

Propagation of shear elastic waves in composites with a random set of spherical inclusions (effective field approach)

The work is dedicated to the problem of plane monochromatic shear wave propagation through elastic matrix composite materials with a homogeneous random set of spherical inclusions. The effective field method (EFM) and quasi-crystalline approximation are used for the calculation of phase velocity and attenuation factor of the mean wave field propagating through the composite. The version of the method developed in the work allows us to obtain the dispersion equation for the wave vector of the mean wave field that serves for all frequencies of the incident field, properties and volume concentrations of the inclusions. The long- and short-wave asymptotic solutions of the dispersion equation are found in closed analytical forms. Numerical solutions of this equation are constructed in a wide region of frequencies that covers the long-, middle- and short-wave regions of the propagating waves. The phase velocities and attenuation factors of the mean wave field in the composites are analyzed for various elastic properties, density and volume concentrations of the inclusions. Comparisons of the predictions of the method with some numerical computation of the effective parameters of matrix composites are presented; possible errors in predictions of the velocities and attenuation factors of the mean wave field in the composites are indicated and discussed.