Twelve shear surface waves guided by clamped/free boundaries in magneto-electro-elastic materials

It is shown that surface waves with 12 different velocities in the cases of different magneto-electrical boundary conditions can be guided by the interface of two identical magneto-electro-elastic half-spaces. The plane boundary of one of the half-spaces is clamped while the plane boundary of the other one is free of stresses. The 12 velocities of propagation of these surface waves are obtained is explicit forms. It is shown that the number of different surface wave velocities decreases from 12 to 2 if the magneto-electro-elastic material is changed to a piezoelectric material.     

Comments on the relation between surface wave theory and the theory of reflection

The sextic Stroh formalism, previously extensively used in the analysis of subsonic phenomena, has been used for the analysis of reflection phenomena and leaky surface waves in the first transsonic range of velocities. In particular the behaviour of the reflection problem at the limiting velocity is studied. It is shown that when the condition of free surface can be satisfied without the inhomogeneous partial wave, a situation which would appear to be the natural limiting case of a surface wave of infinite penetration, the body wave alone satisfies the condition of free surface. This result illuminates the Barnett-Lothe existence theorem for subsonic surface waves. The close connection between the reflection problem and the leaky surface wave problem becomes very apparent in the formalism used. It is shown that for a point on a branch of leaky waves where the solution is undamped, the conditions for simple reflection, i.e. reflection only involving the two body waves, are also present. In the vicinity of such a point reflection is accompanied by resonance excitation of leaky waves. The paper concludes with some explicit calculations for transversely isotropic solids.     

轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

三维缓变流场上波浪折射—绕射的缓坡方程

运用Luke变分原理,建立了波浪在三维缓变流场中和缓变海底上折射-绕射的一般缓坡方程,据此给出了在几何-光学逼近（△↓S)^2=k^2有效时,波浪、环境流和海底坡度必须满足的若干条件,对一般缓坡方程进行了分类,在一种特定流场结构的假定下,得到了方程的行波解。     

Wave propagation in transversely isotropic porous piezoelectric materials

Wave propagation in porous piezoelectric material (PPM), having crystal symmetry 6 mm, is studied analytically. Christoffel equation is derived for the propagation of plane harmonic waves in such a medium. The roots of this equation give four complex wave velocities which can propagate in such materials. The phase velocities of propagation and the attenuation quality factors of all these waves are described in terms of complex wave velocities. Phase velocities and attenuation of the waves in PPM depend on the phase direction. Numerical results are computed for the PPM BaTiO₃. The variation of phase velocity and attenuation quality factor with phase direction, porosity and the wave frequency is studied. The effects of anisotropy and piezoelectric coupling are also studied. The phase velocities of two quasi dilatational waves and one quasi shear waves get affected due to piezoelectric coupling while that of type 2 quasi shear wave remain unaffected. The phase velocities of all the four waves show non-dispersive behavior after certain critical high frequency. The phase velocity of all waves decreases with porosity while attenuation of respective waves increases with porosity of the medium. The characteristic curves, including slowness curves, velocity curves, and the attenuation curves, are also studied in this paper.     

On the existence of the low-frequency surface waves in a porous mediumSur l'existence des ondes de surface basse fréquence en milieux poreux

The existence and propagation of the surface waves at a vacuum/porous medium interface are investigated in the low frequency range. Two types of surface waves are shown to be possible: the generalized Rayleigh wave, which always exists, and the Stoneley wave, which exists for a limited range of wave numbers. Moreover, within the k-domain of existence the Stoneley wave cannot appear for certain values of elastic parameters of the solid phase. The bifurcation behavior of both the Stoneley wave and the Biot (P2) bulk wave, depending on the wave number, is revealed. The asymptotic formulas for the phase velocities of the surface waves are derived. To cite this article: I. Edelman, C. R. Mecanique 332 (2004).     

Numerical study of heat waves excited by oxidation of a magnesium wire

A mathematical model of ignition of Mg particles and wires is proposed. It is based on the concept of thermal deceleration of the chemical reaction responsible for ignition. It is modeled to the experimental data obtained for the dependence of the radius of a Mg particle on the limiting temperature of the gas. A possibility of propagation of heat waves under heterogeneous oxidation of a Mg wire exposed to an external flow is shown. The existence conditions are written for the travelling wave solution and the self-sustained wave regime is found. It is numerically shown that the ignition wave can be initiated by temperature distributions of stepwise initial data and of Gaussian-shaped form. It is shown that self-sustained waves are stable with respect to small and finite disturbances. Received 25 July 1997 / Accepted 13 July 1998     

The propagation of elastic stress waves in a conical shell under axial impulsive loading

The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation due to their different velocities. Southwest Institute of Structural Mechanics     

Propagation and Evolution of Wave Fronts in Two-Phase Porous Media

An investigation is made into the propagation and evolution of wave fronts in a porous medium which is intended to contain two phases: the porous solid, referred to as the skeleton, and the fluid within the interconnected pores formed by the skeleton. In particular, the microscopic density of each real material is assumed to be unchangeable, while the macroscopic density of each phase may change, associated with the volume fractions. A two-phase porous medium model is concisely introduced based on the work by de Boer. Propagation conditions and amplitude evolution of the discontinuity waves are presented by use of the idea of surfaces of discontinuity, where the wave front is treated as a surface of discontinuity. It is demonstrated that the saturation condition entails certain restrictions between the amplitudes of the longitudinal waves in the solid and fluid phases. Two propagation velocities are attained upon examining the existence of the discontinuity waves. It is found that a completely coupled longitudinal wave and a pure transverse wave are realizable in the two-phase porous medium. The discontinuity strength of the pore-pressure may be determined by the amplitude of the coupled longitudinal wave. In the case of homogeneous weak discontinuities, explicit evolution equations of the amplitudes for two types of discontinuity waves are derived.     

On the effects of irregular boundaries in finite difference models

Propagation of periodic waves in the vicinity of irregular saw-tooth shaped boundary in finite difference models is investigated. The reflection of an incoming wave from a single saw-tooth boundary is found to be accompanied by a phase shift. It is shown that any wave mode propagating along such a boundary is trapped and decays in the direction normal to the boundary. A wave propagating along a channel with saw-tooth shaped lateral boundaries is influenced by the trapped waves, which leads to a reduction of the phase velocity. Phase velocities obtained from the present normal mode analysis are compared to velocities in numerical experiments. The agreement is excellent.     

Shock wave in a gas-liquid medium

The propagation of weak shock waves and the conditions for their existence in a gas-liquid medium are studied in [1]. The article [2] is devoted to an examination of powerful shock waves in liquids containing gas bubbles. The possibility of the existence in such a medium of a shock wave having an oscillatory pressure profile at the front is demonstrated in [3] based on the general results of nonlinear wave dynamics. It is shown in [4, 5] that a shock wave in a gas-liquid mixture actually has a profile having an oscillating pressure. The drawback of [3–5] is the necessity of postulating the existence of the shock waves. This is connected with the absence of a direct calculation of the dissipative effects in the fundamental equations. The present article is devoted to the theoretical and experimental study of the structure of a shock wave in a gas-liquid medium. It is shown, within the framework of a homogeneous biphasic model, that the structure of the shock wave can be studied on the basis of the Burgers-Korteweg-de Vries equation. The results of piezoelectric measurements of the pressure profile along the shock wave front agree qualitatively with the theoretical representations of the structure of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 65–69, May–June, 1973.     

Propagation of discontinuity waves in complex rheological media with viscous properties

The propagation of discontinuity waves of various order in rheological media is examined. It is assumed that the region of discontinuity of values can be represented by an intermediate layer of infinitesimal thickness. By means of this representation, results can be obtained for a rather wide class of continuous media with viscous properties, which generalize Duhem's results. The first integrals of the laws of momentum and energy conservation are obtained, which hold inside the intermediate layer at a shock wave.It is shown that when viscosity elements are introduced in a special way into the rheological model of a continuous medium, discontinuity waves of any order are propagated in the medium, and that at the surface of a strong discontinuity in a heat-conducting medium, the temperature is continuous. Additional conditions for strain discontinuities at the viscosity elements are obtained. For certain inclusions of the viscosity elements into the rheological model discontinuity waves do not propagate; instead there is merely a weak discontinuity surface which acts as an interface between the flow region of the continuous medium and the region in the state of rest. Contact discontinuities can occur in any continuous medium.The possible existence of a geometrical discontinuity surface in a viscous gas was examined first by Duhem [1]. He established that singluar strong-discontinuity surfaces cannot take place in a viscous gas. However, if one assumes that the velocity and temperature are continuous in the passage through a singular surface, only contact discontinuities are possible [2].     

An analytical approach to reconstruction of axisymmetric defects in pipelines using T(0, 1) guided waves

Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission. Especially, the torsional mode T(0, 1), which is the first order of torsional guided waves, plays the irreplaceable position and role, mainly because of its non-dispersion characteristic property. However, one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipeli...     

The Peculiarities of Linear Wave Propagation in Double Porous Media

The features of propagation of longitudinal and transverse waves (LW and TW) in fractured porous medium (FPM) saturated with liquid are investigated by methods of multiphase mechanics. The mathematical model of FPM accounting for inequality of velocities and pressures of liquid in pores and fractures, liquid mass exchange and nonstationary interaction forces is developed. Processes of monochromatic wave propagation are studied. The dispersion relation is obtained and the effect of model parameters on wave propagation is analysed. It is established that one transverse and three longitudinal waves propagate in FPM saturated with liquid. The fastest LW is a deformational wave and the two others are filtrational. Filtrational waves attenuate much stronger than deformational and transverse waves. Distinction of velocities and pressures in liquid in various pore systems provides an explanation for the existence of the two filtrational waves in porous medium with two different characteristic sizes of pores.     

Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids

Wave propagation in a porous elastic medium saturated by two immiscible fluids is investigated. It is shown that there exist three dilatational waves and one transverse wave propagating with different velocities. It is found that the velocities of all the three longitudinal waves are influenced by the capillary pressure, while the velocity of transverse wave does not at all. The problem of reflection and refraction phenomena due to longitudinal and transverse wave incident obliquely at a plane interface between uniform elastic solid half-space and porous elastic half-space saturated by two immiscible fluids has been analyzed. The amplitude ratios of various reflected and refracted waves are found to be continuous functions of the angle of incidence. Expression of energy ratios of various reflected and refracted waves are derived in closed form. The amplitude ratios and energy ratios have been computed numerically for a particular model and the results obtained are depicted graphically. It is verified that during transmission there is no dissipation of energy at the interface. Some particular cases have also been reduced from the present formulation.     

Surface waves under constrained deformation

The possibility of the existence of surface waves in a range of velocities greater than the velocity of transverse waves, but smaller than the velocity of longitudinal waves is shown. It turns out that, in the boundary value problem for an elastic half-space in this velocity range, there are the surface waves whose velocity is constant and equal to \(\sqrt 2 \) b, where b is the velocity of transverse waves. These waves as well as the Rayleigh surface waves have no dispersion. Their velocity is specified only by the elastic constants and density of the medium. It is also shown that the existence of such a velocity is possibly related to the velocity of surface waves that appear as unloading waves under constrained deformation.     

Piezoelectromagnetic waves in a ceramic plate between two ceramic half-spaces

We analyze the propagation of piezoelectromagnetic waves guided by a plate of polarized ceramics between two ceramic half-spaces. An exact dispersion relation is obtained, which reduces to a few known elastic, electromagnetic, and quasistatic piezoelectric wave solutions in the literature as special cases. Numerical solutions to the equation that determines the dispersion relation show the existence of guided waves. The results are useful for acoustic wave and microwave devices.     

Theoretical transient analysis and wave propagation of piezoelectric bi-materials

The transient response of piezoelectric bi-materials subjected to a dynamic anti-plane concentrated force or electric charge with perfectly bonded interface is examined in the present study. The problem is solved by using the Laplace transform method and the inverse Laplace transform is evaluated by means of Cagniard’s method. Exact transient full-field solutions of the contribution for each wave are expressed in explicit closed forms. The transient behavior of field quantities is examined in detail by numerical calculations. The existence condition of a propagating surface wave along the interface is discussed in detail. A surface wave can be guided by the interface of two semi-infinite materials in contact if one, at least, of these two materials is piezoelectric. The propagation velocity of the surface wave is explicitly expressed and is found to be less than the lower shear wave velocity of the two materials. The existence of the surface wave for piezoelectric–piezoelectric bi-materials is restricted to the situation that the shear waves of the two piezoelectric materials are very close. The possibility for the existence of the surface wave for piezoelectric–elastic bi-materials is much greater than that of the piezoelectric–piezoelectric bi-materials.     

On diffraction of acoustic and electric waves in piezoelectric medium by an absorbent half-plane electrode

Diffraction of incident acoustic and incident electric waves in a transversally isotropic piezoelectric medium at the boundary of a half-plane absorbent electrode is systematically investigated using the quasi-hyperbolic approximation. The electrode is assumed to be very thin so that its thickness and stiffness can be neglected. By exact inversion, the explicit expressions for the scattering waves are obtained. A closed form solution is obtained by applying Laplace transformations and the Wiener–Hopf technique. By means of the Cagniard–de Hoop method a detailed investigation of the structure of the electro-acoustic wave is conducted. The mode conversion between electric and acoustic waves, the effect of electro-acoustic head wave, the Bleustein–Gulyaev surface wave and the structure of the wave in terms of the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in detail. It is shown that in piezoelectric materials, absorbent electrodes are neither completely opaque nor completely transparent to electric and acoustic waves. The dynamic field intensity factors at the tip of the electrode are functions of the angle of incidence and time; they are derived explicitly and discussed through a detailed numerical analysis.