Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer

This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic monoclinic semi-infinite media. Dispersion equation is obtained in a closed form. In the absence of magnetic field and irregularity of the medium, the dispersion equation agrees with the equation of classical case in three layered media. The effects of magnetic field and size of irregularity on the phase velocity are depicted by means of graphs.     

Effect of irregularity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer

The paper studies the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity is taken in the half space in the form of a rectangle. It is observed that torsional surface waves propagate in this assumed medium. In the absence of the irregularity, the velocity equation of the torsional surface wave is also obtained. For a layer over a homogeneous half space, the velocity of torsional surface waves coincides with that of the Love waves.     

Surface electro-elastic shear horizontal waves in a layered structure with a piezoelectric substrate and a hard dielectric layer

The existence and behaviour of surface electro-elastic shear horizontal waves in a layered structure consisting of a piezoelectric substrate of crystal class 6, 4, 6mm, or 4mm mechanically bonded at its upper surface to an elastic dielectric layer and bounded by an adjacent dielectric medium is considered when the shear bulk wave velocity in the elastic layer is greater than or equal to that in the substrate. The dispersion equation for the existence of the surface electro-elastic SH waves with respect to the phase velocity is obtained which 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 investigation of the solutions of the dispersion equation is carried out and all the possible cases of the behaviour of the surface electro-elastic SH wave depending on the electro-mechanical coefficients of the layered structure are revealed.     

SHEAR-HORIZONTAL WAVES IN A ROTATED Y-CUT QUARTZ PLATE WITH AN ISOTROPIC ELASTIC LAYER OF FINITE THICKNESS

We study shear-horizontal (SH) waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elast...     

Shear horizontal waves in transversely inhomogeneous plates

Shear horizontal (SH) waves in free and clamped monoclinic plates with an arbitrary inhomogeneity across the plate are considered. Firstly, some general properties of dispersion spectra of, specifically, the SH waves are pointed out. Secondly, analytical and numerical modeling of the SH dispersion branches is presented. Closed-form estimations are compared with exact curves computed for a free plate with continuously varying properties.     

梯度介质半空间Rayleigh面波传播性能研究

对剪切弹性模量沿深度以指数函数变化的非均质半空间，本文用摄动法得到了Rayleigh面波的波函数解答及相速度方程。以不同金属与陶瓷复合而成的几种梯度材料为例，用数值方法求解了相速度方程，给出了相应的波的弥散曲线，结果表明，梯度介质半空间自由表面附近的Rayleigh波通常有两种不同的弥散形式，即正常弥散和非正常弥散。     

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano’s and Ferrari’s methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.     

Decaying surface waves in inhomogeneous media

Two problems on plane decaying surface waves in an inhomogeneous medium are under consideration: the problem where the waves similar to Rayleigh waves propagate in an isotropic elastic half-space that borders with a layer of an ideal incompressible fluid and the problem where the waves similar to Love waves propagate in a semi-infinite saturated porous medium that borders with a layer of an isotropic elastic medium.     

Propagation of torsional waves in an inhomogeneous layer over an inhomogeneous half-space

The present paper is concerned with the study of propagation of torsional waves in an inhomogeneous isotropic layer whose material properties vary harmonically with a space variable, lying over a semi-infinite inhomogeneous isotropic half-space. The closed form solutions for the displacement in the layer and half-space are obtained separately. The dimensionless phase velocity has been plotted against dimensionless wave number and scaled wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves using 2D and 3D plot.     

弱界面压电／压磁层状结构中的SH波

研究了弱界面压电层/压磁半空间结构中SH波的频散特性, 界面性能由 ``弹簧'模型表征, 压电层的表面考虑电学短路和电学开路两种边界条件. 推导了显函形式的 频散方程, 并结合算例分析了界面性能和电学边界条件对SH波传播特性的影响. 数值结果表 明: 弱界面降低了SH波传播的相速度; 对于短路电边界条件, 弱界面可以使一阶模态的相速 度小于B-G表面波的速度; 对于开路电边界条件, 一阶模态的相速度总是大于剪切体波的波 速.     

Scattering of elastic waves by three-dimensional surface topographies

Diffraction of plane harmonic waves by three-dimensional surface irregularities is investigated through the use of an indirect boundary integral equation method. The irregularity of an arbitrary shape is embedded in an elastic half-space and subjected to incident P, SV, SH, and Rayleigh waves. The material of the half-space is assumed to be linear, weakly anelastic, homogeneous and isotropic.

The accuracy of the method is demonstrated through comparison of the results with existing axisymmetric solutions. Several numerical examples for non-axisymmetric canyons are presented. The resulting amplification patterns exhibit strong sensitivity on type and angle of the incident waves and on the location of the observation point. Systematic comparisons of three-dimensional and corresponding two-dimensional models demonstrate similarity of the amplification pattern. The amplification is larger in some three-dimensional models than in two-dimensional ones. Strong coupling between SH and P-SV modes is observed for off-azimuthal incident waves. This phenomenon is specially pronounced for incident SH waves and it is intrinsic to three-dimensional scattering.     

SH-waves in viscoelastic heterogeneous layer over half-space with self-weight

The effect of gravity, heterogeneity and internal friction on propagation of SH-waves (horizontally polarised shear waves) in viscoelastic layer over a half-space has been studied. Using the method of separation of variables, dispersion equation has been obtained and used to recover the damped velocity of SH-waves. Both the real and imaginary parts of dispersion equation are in well agreement with the classical Love wave equation. It has been observed that heterogeneity of the medium affects the velocity profile of SH-wave significantly. Some other peculiarities have been observed and discussed in our study.     

非理想界面弹性层/压电柱结构中SH波的传播特性

研究了各向同性弹性层与压电柱之间非理想连接时沿周向传播的SH波的频散特性.弹性层表面力学自由;弹性层与压电柱之间应力连续、位移间断.通过求解控制方程,将问题的解用Bessel函数表示,利用界面条件和边界条件得到频散方程,然后对其进行数值求解,分析了界面性态、材料常数和几何尺寸对SH波传播特性的影响.     

Squirt-Flow in Fluid-Saturated Porous Media: Propagation of Rayleigh Waves

Propagation of attenuated waves is studied in a squirt-flow model of porous solid permeated by two different pore regimes saturated with same viscous fluid. Presence of soft compliant microcracks embedded in the grains of stiff porous rock defines the double-porosity formation. Microcracks and pores respond differently to the compressional effect of a propagating wave, which induces the squirt-flow from microcracks to pores. Elastodynamics of constituent particles in porous aggregate is represented through a single-porosity formulation, which involves the frequency-dependent complex moduli. This formulation is deduced as a special case of double-porosity formation allowing the wave-induced flow of pore-fluid. This squirt-flow model of porous solid supports the attenuated propagation of two compressional waves and one shear wave. Superposition of these body waves, subject to stress-free surface, defines the propagation of Rayleigh wave. This wave is governed by a complex irrational dispersion equation, which is solved numerically after rationalising into an algebraic equation. For existence of Rayleigh wave, a complex solution of the dispersion equation should represent a leaky wave, which decays for propagation along any direction in the semi-infinite medium. A numerical example is solved to analyse the effects of squirt-flow on phase velocity, attenuation and polarisation of the Rayleigh waves, for different combinations of parameters. Numerical results suggest the existence of an additional (second) Rayleigh wave in the squirt-flow model of dissipative porous solids.     

Linear theory of gravity waves on a Voigt viscoelastic medium

Linear surface gravity waves on a semi-infinite incompressible Voigt medium are studied in this paper. Three dimensionless parameters, the dimensionless viscoelastic parameter ϑ, the dimensionless wave number and the dimensionless surface tension are introduced. A dimensionless characteristic equation describing the waves is derived. This is a sixth order complex algebraic equation which is solved to give the complex dispersion relation. Based on the numerical solution, two critical values of ϑ, ϑ _A =0.607 and ϑ _B =2.380, which represent the appearance of the cutoff region and the disappearance of the strong dispersion region, are found. The effects of ϑ on the characteristic equation and the properties of the waves are discussed. The project supported by the National Natural Science Foundation of China (59709006)     

Dispersion in oceanic crust during earthquake preparation

Dispersion of Stoneley waves is studied in a sedimentary layer of ocean bottom resting over basaltic solid half space. Sedimentary layer is assumed a transversely isotropic poroelastic medium. Lower-most solid half-space is assumed to be embedded with vertically aligned saturated micro-cracks and behaves transversely isotropic to wave propagation.Frequency equation is obtained in the form of determinantal equation. Role of phase angle is eliminated by expressing slowness of waves in terms of phase velocity and elastic constants. Numerical solutions for phase velocity and group velocity are obtained for a particular model. Calculations are made for different depths of ocean and sediments. Effect of thickness and density of cracks on these velocities are observed.Special cases are discussed which represent the absence of ocean and sediments, in the model considered. Changes in dispersion are discussed during the stress accumulation in an earthquake preparation region.     

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.     

Propagation behavior of SH waves in a piezomagnetic substrate with an orthorhombic piezoelectric layer

The dispersion behavior of the shear horizontal (SH) waves in the coupled structure consisting of a piezomagnetic substrate and an orthorhombic piezoelectric layer is investigated with different cut orientations. The surface of the piezoelectric layer is mechanically free, electrically shorted, or open, while the surface of the piezomagnetic substrate is mechanically free, magnetically open, or shorted. The dispersion relations are derived for four electromagnetic boundary conditions. The dispersion characteristics are graphically illustrated for the layered structure with the PMN-PT layer perfectly bonded on the CoFe₂O₄ substrate. The effects of the PMN-PT cut orientations, the electromagnetic boundary conditions, and the thickness ratio of the layer to the substrate on the dispersion behavior are analyzed and discussed in detail. The results show that, (i) the effect of the cut orientation on the dispersion curves is very obvious, (ii) the electrical boundary conditions of the PMN-PT layer dominate the propagation feature of the SH waves, and (iii) the thickness ratio has a significant effect on the phase velocity when the wave number is small. The results of the present paper can provide valuable theoretical references to the applications of piezoelectric/piezomagnectic structure in acoustic wave devices.     

功能梯度压电夹层结构中SH波的传播

研究了功能梯度压电上、下半空间和均匀压电层组成的夹层结构中SH波的传播性能,上、下功能梯度半空间的材料性能沿垂直于界面方向以指数函数形式变化。首先推导了SH传播时电弹场的解析解,然后利用界面条件得到了行列式形式的频散方程。基于推导的频散方程,通过数值算例表明了材料性能梯度变化、压电层厚度和材料组合方式对相速度的影响,结果对功能梯度压电材料在声波器件中的应用有参考价值。     

Nondispersive wave propagation in a layered composite

It is found that it is possible to propagate a horizontally polarized (SH) wave without dispersion through an elastic, periodically-layered composite. The nondispersive property of the wave is due to the fact that at each interface the angle of incidence is such that the wave is totally transmitted without reflection. In optics such an angle is referred to as the Brewster angle. It is determined that this particular case is contained as a special solution of the general dispersion equation for SH waves, which has not been noticed before.