Surface waves in magneto-elastic initially stressed conducting media

Summary The object of the present paper is to investigate the magneto-elastic surface waves in an initially stressed conducting medium. The theory of magneto-elastic surface waves in an initially stressed conducting medium has firstly been deduced and then it has been employed in investigating the particular cases of surface waves such as (i) Rayleigh waves (ii) Love waves and (iii) Stoneley waves. The wave-velocity equations obtained in different cases are in agreement with the corresponding classical results when the solid is initially unstressed and the magnetic field is absent or the material is non-magnetic.     

OnLamb's problem: Line load suddenly applied in a magneto-elastic initially stressed conducting half-space

Summary The paper is concerned with the investigation of the plane Lamb's problem in which a line load is suddenly applied on a magneto-elastic initially stressed conducting half-space bounded by a plane. The results obtained in this investigation are in agreement with the corresponding results of the classical plane Lamb's problem when the semispace is supposed to be initially unstressed and non-magnetic.     

Onlamb's problem in a magneto-elastic initially stressed conducting medium

Summary The object of the present paper is to investigate the so-called planeLamb's problem in an initially stressed magneto-elastic semi-space bounded by a plane. The results obtained in this investigation are in agreement with the corresponding results of the classical planeLamb's problem when the semi-space is supposed to be initially unstressed and non-magnetic.     

Magneto-elastic waves in an initially stressed conducting elastic layer

Summary The paper deals with the propagation of waves in a magneto-elastic initially stressed conducting layer. The wave velocity equation obtained is in agreement with the classical result of Rayleigh and Lamb when the layer is initially unstressed and the magnetic field isabsent.     

Steady state response to moving loads in a magneto-elastic initially stressed conducting medium

Summary Investigated is the steady state response to moving loads in an initially stressed magneto-elastic half-space bounded by a plane. The results obtained in this problem are in agreement with the corresponding classical results when the half space is supposed to be initially unstressed and non-magnetic.     

Magneto-elastic waves and disturbances in initially stressed conducting media

Summary The object of the present paper is to investigate magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, the theory of magneto-elastic surface waves in a conducting medium under an initial uniaxial tension has been deduced and then it has been employed to investigate the particular cases of surface waves such as Rayleigh, Love and Stoneley waves. Secondly, propagation of waves in an elastic layer has been considered using the fundamental equations of motion for magneto-elastic waves in conductors under an initial uniaxial tension or compression. This is followed by the case of plane Lamb's problem in a magneto-elastic semi-space under the same initial tension. The final results obtained in the above cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

On the propagation of magneto-elastic waves

Summary The electromagnetic equations of Maxwell, equations of elasticity have been used to solve the problem of propagation of waves for a one-dimensional magneto-elastic problem. The frequency equation has also been set forth.     

Effect of surface stress on magneto-elastic surface waves in finitely conducting media

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as obtained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.     

Magneto-elastic waves and disturbances in initially stressed conducting media: II

Summary The paper is concerned with the investigation of the magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, (a) the steady state response to moving loads in a magneto-elastic initially stressed conducting medium under an uniaxial tension has been discussed. Secondly, (b) the Lamb's problem corresponding to a line load suddenly applied in a magneto-elastic initially stressed conducting half-space bounded by a plane under uniaxial tension has been investigated. The final results obtained in both cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.     

Reflection and transmission of plane SH-waves in an initially stressed inhomogeneous anisotropic magnetoelastic medium

This study investigates the reflection and transmission of plane SH-waves in two semi-infinite anisotropic magnetoelastic media. The lower half-space is considered as initially stressed and inhomogeneous. The density of lower half-space is taken exponentially varying with depth. The solutions for half-spaces are obtained analytically. The expressions for reflection and transmission coefficient are obtained in the closed form subject to continuity conditions at the interfaces of anisotropic magnetoelastic half-spaces and the Snell’s law. It is found that these coefficients depend on the initial stress, inhomogeneity parameter, the magnetoelastic coupling parameter, and the angle at which wave crosses the magnetic field of the half-spaces. Numerical computations are performed for these coefficients for a specific model of two different anisotropic magnetoelastic half-spaces. The numerical results are illustrated by the graph of reflection and transmission coefficient versus the angle of incidence. In general, as the initial stress increases the reflection and transmission coefficient increases, the affect is more prominent for more than 10 GPa. Inhomogeneity in the density of the material also increases the reflection and transmission coefficient. The anisotropic magnetoelastic parameter and the angle at which the wave crosses the magnetic field for both the half-spaces have a quite significant effect on the reflection and transmission coefficient.     

Modifications of the dispersion relations for surface waves in a layer on a half-space

Summary Dispersion relations for Love and Rayleigh waves in a layer on a half-space are modified by introducing quadratic slownesses instead of velocities. The advantages of this approach are demonstrated on analytical formulae for computing the group velocity.     

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green’s functions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of fictitious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary...     

平面SV波在层状半空间中沉积谷地周围的散射

采用间接边界元方法求解了入射平面SV波在层状半空间中沉积谷地周围的散射问题.问题的解答包含自由场和散射场两部分.自由场可由直接刚度法求得,散射场由层状半空间中斜线荷载动力格林函数来模拟.文中以入射平面SV波在基岩上单一土层中沉积谷地周围散射为例研究了土层和沉积谷地周围的影响.结果表明,由于考虑了土层的动力特性,平面SV...     

平面SV波在饱和半空间中沉积谷地周围的散射

采用一种特殊的间接边界积分方程法,求解了平面SV波在饱和半空间中任意形状沉积谷地周围的二维散射问题。结合饱和半空间中膨胀波源和剪切波源格林函数,由分布在沉积和半空间交界面附近两虚拟波源面上的波源分别构造沉积内外的散射波场,由交界面连续条件建立方程并求解确定虚拟波源密度,总波场反应即可由自由波场和散射波场叠加而得。然后通过边界条件验算、退化解答与现有结果的比较以及稳定性检验,验证了方法的计算精度。通过一组典型算例,研究了平面SV波在饱和半空间中沉积谷地周围散射的基本规律,详细给出了不同参数情况沉积谷地附近地表位移幅值和孔隙水压,着重分析了入射SV波频率和角度、边界渗透条件、沉积孔隙率等因素对场地反应的影响,得出了一些有益的结论。     

SH waves in stressed elastic plates

Summary A theoretical study is made of the propagation ofSH waves of small amplitude in an infinite elastic plate subjected to a primary normal stress. It is shown that the effect of the stress may be represented by a re-scaling of the plate thickness, provided that one elastic constant is also redefined suitably.     

Axisymmetric transient waves in transversely isotropic half-space

A transversely isotropic material in the sense of Green is considered. Using a series of potential functions proposed in [Eskandari-Ghadi M. A complete solution of the wave equations for transversely isotropic media. J Elasticity 2005; 81:1–19], the solutions of the transient wave equations within a half-space under surface load are obtained in the Laplace–Hankel domain for axisymmetric problems. The solutions are investigated in detail in the special case of a surface point force pulse varying with time as Heaviside function. Using Cagniard–De Hoop method, the inverse Laplace transform and inverse Hankel transform of the solutions are then obtained in the form of integrals with finite limits. For validity of the analytical results, the final formulations for surface waves are degenerated for an isotropic material and compared with the existing formulation obtained by Pekeris [The seismic surface pulse. Proc Natl Acad Sci USA 1955;41:469–80], to show that they are exactly the same. The numerical evaluations of the integrals for some transversely isotropic materials as well as an isotropic one are obtained. The present approach is then numerically verified by comparing a particular case of displacements for the surface of an isotropic half-space subjected to a point load of Heaviside function with the solutions obtained by Pekeris [The seismic surface pulse. Proc Natl Acad Sci USA 1955;41:469–80]. In addition, the wave equations for the mentioned medium are obtained on the vertical line directly under the applied surface load. The final formulations are degenerated for an isotropic material and compared with the existing formulation given in Graff [Wave motion in elastic solids. New York: Dover Publications Inc; 1975 [New Ed edition, November 1991]], to show that they are also exactly the same. Then equations are presented in graphical forms using an appropriate numerical evaluation.     

ASH-source in an elastic half-space with a non-homogeneous surface layer

Summary The response of an elastic half-space with a non-homogeneous surface layer due to aSH-source operating in the non-homogeneous layer of an elastic half-space have been studied. The elastic and physical constants vary exponentially in the surface layer. The surface displacement consists of several integrals. On approximate evaluation of these integrals, they are identified as direct or reflected pulses.