Thermoelastic surface waves on an exponentially graded half-space

In this paper, we consider the propagation of Rayleigh surface waves in a functionally graded isotropic thermoelastic half-space, in which all thermoelastic characteristic parameters exponentially change along the depth direction. The propagation condition is established in the form of a bicubic equation whose coefficients are complex numbers while the analytical solutions (eigensolutions) of the thermoelastodynamic system are explicitly obtained in terms of the characteristic solutions. The concerned solution of the Rayleigh surface wave problem is subsequently expressed as a linear combination of the three eigensolutions while the secular equation is established in an implicit form. The explicit secular equation is written when an isotropic and homogeneous thermoelastic half-space is considered and some numerical simulations are given for a specific material.     

On the propagation waves in the theory of thermoelasticity with microtemperatures

The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasi-thermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.     

Rayleigh waves in orthotropic fluid-saturated porous media

In this paper, we are interested in the propagation of Rayleigh waves in orthotropic fluid-saturated porous media. This problem was investigated by Liu and Liu (2004). The authors have derived the secular equation of the wave but that secular equation is still in implicit form. The main aim of this paper is to derive explicit secular equation of the wave. By employing the method of polarization vector, the secular equations of Rayleigh waves in explicit form is obtained. This equation recovers the dispersion equation of Rayleigh waves propagating in pure orthotropic elastic half-spaces. Remarkably, the secular equation obtained is not a complex equation as the one derived by Liu and Liu, it is a really real equation.     

Rayleigh Surface Waves on a Kelvin-Voigt Viscoelastic Half-Space

In this paper we consider the propagation of Rayleigh surface waves in an exponentially graded half-space made of an isotropic Kelvin-Voigt viscoelastic material. Here we take into account the effect of the viscoelastic dissipation energy upon the corresponding wave solutions. As a consequence we introduce the damped in time wave solutions and then we treat the Rayleigh surface wave problem in terms of such solutions. The explicit form of the secular equation is obtained in terms of the wave speed and the viscoelastic inhomogeneous profile. Furthermore, we use numerical methods and computations to solve the secular equation for some special homogeneous materials. The results sustain the idea, existent in literature on the argument, that there is possible to have more than one surface wave for the Rayleigh wave problem.     

Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact

In the present paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate, yet highly accurate secular equation of fourth-order in terms of the dimensionless thickness of the layer is derived. From the secular equation obtained, an approximate formula of third-order for the velocity of Rayleigh waves is established. The approximate secular equation and the formula for the velocity obtained in this paper are potentially useful in many practical applications.     

Rayleigh waves in anisotropic porous media and the polarization vector method

In this paper, the propagation of Rayleigh waves in orthotropic non-viscous fluid-saturated porous half-spaces with sealed surface-pores and with impervious surface is investigated. The main aim of the investigation is to derive explicit secular equations and based on them to examine the effect of the material parameters and the boundary conditions on the propagation of Rayleigh waves. By employing the method of polarization vector the explicit secular equations have been derived. These equations recover the ones corresponding to Rayleigh waves propagating in purely elastic half-spaces. It is shown from numerical examples that the Rayleigh wave velocity depends strongly on the porosity, the elastic constants, the anisotropy, the boundary conditions and it differs considerably from the one corresponding to purely elastic half-spaces. Remarkably, in the fluid saturated porous half-spaces, Rayleigh waves may travel with a larger velocity than that of the shear wave, a fact that is impossible for the purely elastic half-spaces.     

Wave propagation in thermally conducting linear fibre-reinforced composite materials

The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves. The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared to those without thermal disturbances and anisotropy parameters.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Elasto-thermodiffusive (ETNP) surface waves in semiconductor materials

The present article is devoted to investigate the propagation of elasto-thermodiffusive (ETNP) surface waves in a homogeneous isotropic, thermally conducting semiconductor material of half-space with relaxation of heat and charge carrier fields. The secular equation, a more general functional relation, that governs the propagation of elasto-thermodiffusive (ETNP) surface waves in homogeneous isotropic, thermoelastic semiconductor material halfspace with relaxation of heat and charge carrier fields has been derived by solving a system of coupled partial differential equations. A hybrid numerical technique consisting of Descartes algorithm for solving complex polynomial characteristic equation along with functional iteration scheme has been successfully used to solve the secular equation in order to obtain dispersion curves, attenuation coefficient and specific loss factor of energy dissipation for p-type germanium (Ge) semiconductor. Some particular forms of the general secular equation governing the propagation of elasto-thermodiffusive (ETN/ETP), thermoelastic (ET), elastodiffusive (EP/EN) and thermodiffusive (TP/TN) surface waves have been also deduced and discussed. In order to illustrate the analytical development, the numerical solution of the secular equation and other relevant relations under different situations is also carried out for Ge semiconductor materials to characterize the elasto-thermodiffusive (ETP) and thermodiffusive (TP) surface waves. The computer simulated results have been presented graphically in respect of the dispersion curves, attenuation coefficient and specific loss factor.     

Rayleigh waves in an incompressible elastic half-space overlaid with a water layer under the effect of gravity

This paper is concerned with the propagation of Rayleigh waves in an incompressible isotropic elastic half-space overlaid with a layer of non-viscous incompressible water under the effect of gravity. The authors have derived the exact secular equation of the wave which did not appear in the literature. Based on it the existence of Rayleigh waves is considered. It is shown that a Rayleigh wave can be possible or not, and when a Rayleigh wave exists it is not necessary unique. From the exact secular equation the authors arrive immediately at the first-order approximate secular equation derived by Bromwich [Proc. Lond. Math. Soc. 30:98–120, 1898]. When the layer is assumed to be thin, a fourth-order approximate secular equation is derived and of which the first-order approximate secular equation obtained by Bromwich is a special case. Some approximate formulas for the velocity of Rayleigh waves are established. In particular, when the layer being thin and the effect of gravity being small, a second-order approximate formula for the velocity is created which recovers the first-order approximate formula obtained by Bromwich [Proc. Lond. Math. Soc. 30:98–120, 1898]. For the case of thin layer, a second-order approximate formula for the velocity is provided and an approximation, called global approximation, for it is derived by using the best approximate second-order polynomials of the third- and fourth-powers.     

Free vibration of microstretch thermoelastic plate with one relaxation time

The propagation of waves in microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT) and Lord and Shulman (L–S) theories of thermoelasticity. The secular equations for both symmetric and skew-symmetric wave mode propagation have been obtained. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation. The amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew symmetric wave modes are computed analytically and presented graphically for different theories of thermoelasticity. The theoretical and numerical computations are found to be in close agreement.     

Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate

The constitutive relations and field equations for anisotropic generalized thermoelastic diffusion are derived and deduced for a particular type of anisotropy, i.e. transverse isotropy. Green and Lindsay (GL) theory, in which, thermodiffusion and thermodiffusion–mechanical relaxations are governed by four different time constants, is selected for study. The propagation of plane harmonic thermoelastic diffusive waves in a homogeneous, transversely isotropic, elastic plate of finite width is studied, in the context of generalized theory of thermoelastic diffusion. According to the characteristic equation, three quasi-longitudinal waves namely, quasi-elastodiffusive (QED-mode), quasi-massdiffusive (QMD-mode) and quasi-thermodiffusive (QTD-mode) can propagate in addition to quasi-transverse waves (QSV-mode) and the purely quasi-transverse motion (QSH-mode), which is not affected by thermal and diffusion vibrations, gets decoupled from the rest of the motion of wave propagation. The secular equations corresponding to the symmetric and skew symmetric modes of the plate are derived. The amplitudes of displacements, temperature change and concentration for symmetric and skew symmetric modes of vibration of plate are computed numerically. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient and amplitudes of wave propagation are presented graphically in order to illustrate and compare the analytically results. Some special cases of frequency equation are also deduced from the existing results.     

川藏公路地质环境与整治改建方案的思考

川藏公路由于地质环境复杂、建设标准低、后遗病害多,抗灾能力差,泥石流、滑坡、山崩、雪害、水毁等自然灾害频繁发生,公路阻车断道严重。国家投入巨资进行整治改建,并取得了明显的效果,但由于自然环境特殊、影响因素复杂,许多特大型、大型工程地质病害问题还没有可行、可靠的解决方案。本文通过分析川藏公路沿线的地质环境和灾害特点,总结历年整治改建和经验的教训,提出川藏公路建设的途径、可能达到的目标和应采用的原则。     

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.     

热冲击下物性与温度相关性对热弹性响应的渐进分析

计及材料物性与温度的相关性,基于Green-Naghdi能量无耗散广义热弹性理论(G-N II理论),对热冲击下具有变物性特征材料的热弹性响应进行了求解分析。借助Laplace正、反变换技术以及Krichhoff变换,在热物性参数随真实温度呈线性规律的前提下,推导了半无限大体受热冲击作用时热弹性响应的解析表达式,通过求解分析,得到了热冲击下热波、热弹性波的传播规律,位移场、温度场以及应力场的分布情况,以及物性随温度相关性对热弹性响应的影响效果。结果表明：当考虑材料物性随温度的变化时,热波、热弹性波的传播以及各物理场的分布均受到不同程度的影响,且物性随温度相关性对热弹性响应的作用效果将受到材料热-力耦合特性的影响。     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

Surface waves in deformed Bell materials

Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain. The surface wave propagates in a principal direction of strain and is attenuated in another principal direction, orthogonal to the free surface. For these waves, the secular equation giving the speed of propagation is established by the method of first integrals. This equation is not the same as the secular equation for incompressible half-spaces, even though the Bell constraint and the incompressibility constraint coincide in the isotropic infinitesimal limit.     

Rayleigh lamb waves in micropolar isotropic elastic plate

The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit, the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.     

曲面曲率对Rayleigh波传播特性的影响

对任意形状的均匀各向同性线弹性曲面物体,用 WKB～（1）方法求解了沿曲面传播的Rayleigh表面波的运动微分方程,同时考虑了波传播方向及其垂直方向曲面曲率对波的穿透性的影, 所获波动方程的势函数解答表明,在一般情况下垂直波传播方向的曲面曲率对波的穿透深度的影响是不容忽视的.进而以同种介质平面表面情况下的Rayleigh面波的传播特性为基准,给出了曲面曲率引起波数或波速变化的解析表达式.通过理论分析和数值算例,描述了曲面上Rayleigh面波传播行为的一些基本特征.