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.     

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.     

初始应力及磁场作用下导电粘弹体内的平面波

本文研究初始应力及磁场作用下导电粘弹体内的波动特性。首先导出有初始应力及磁场作用下导电粘弹体运动的基本方程,然后用它去研究流体静压力及单轴初始应力下波动方程的解,从平面简谐波的频散方程,分析了初始应力及磁场对波动传播的影响。粘弹体用Kelvin-Voigt模型,外磁场假定为均匀。所得结果表明,初始应力对波的影响随应力性质不同而有所差异,它既影响波的相速也影响波的衰减。磁场影响的大小决定于外磁场的强弱。从本文所得公式中,令外磁场为零,可得初始应力对波特性的影响;如令初始应力为零,就得到磁场对波的影响结果;令两者同时为零,即得粘弹波的经典结果。     

初始应力及磁场作用下导电粘弹体内的平面波

本文研究初始应力及磁场作用下导电粘弹体内的波动特性。首先导出有初始应力及磁场作用下导电粘弹体运动的基本方程,然后用它去研究流体静压力及单轴初始应力下波动方程的解,从平面简谐波的频散方程,分析了初始应力及磁场对波动传播的影响。粘弹体用Kelvin-Voigt模型,外磁场假定为均匀。所得结果表明,初始应力对波的影响随应力性质不同而有所差异,它既影响波的相速也影响波的衰减。磁场影响的大小决定于外磁场的强弱。从本文所得公式中,令外磁场为零,可得初始应力对波特性的影响;如令初始应力为零,就得到磁场对波的影响结果;令两者同时为零,即得粘弹波的经典结果。     

在初始应力作用下磁热粘弹波的传播

本文研究在初始应力作用下导热导电粘弹体内平面波的传播.首先导出有初始应力存在时电磁场、位移场、温度场所满足的基本方程然后用它研究了流体静压力或张力及单轴压或张的初始应力条件下,磁——热——粘弹平面波的传播特性.讨论了弱耦合情况下,热效应磁场对波传播特性的影响.在无初始应力存在并略去热、磁耦合效应时,所得结果变成经典的粘弹波结果.     

Magneto-elastic plane waves in a cosserat medium

Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.     

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.     

Propagation of Rayleigh waves on cylindrical surfaces of transversely isotropic material and of varying density in a magnetic field

Summary Three dimensional magneto-elastic equations pertaining to the problem of propagation of axial Rayleigh waves on the surface of elastic cylinder of isotropic material have been solved. Two cases have been considered — first, when the density varies linearly and second, when it varies inversely as the radius vector and frequency equations for both the cases have been obtained.     

Magneto-elastic love waves

Summary The propagation of Love waves under the influence of an externally applied magnetic field is studied. The general phase velocity equation is derived and two special cases when the magnetic field is aligned with and transverse to the direction of wave propagation are discussed. in these cases, it is found that the magneto-elastic problem in hand can be reduced to the corresponding problem in pure elasticity.     

Propagation ofSH waves in an infinite elastic plate with Cauchy's initial transverse stress

Summary Cauchy theory of initial stress has been applied to investigate the problem of SH waves in an initialy stressed elastic plate. The initial stress is assumed to be a uniform tension or compression along the thickness of the plate. It is found that the initial stress influences the velocities of the dispersive modes only but, it has no influence on the velocity of the non-dispersive wave.     

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.     

On the generation of capillary-gravity waves due to two-dimensional sources

Summary With the aid of the generalized function method, a study is made of the linearized theory of transient development of capillary-gravity waves in an inviscid, incompressible and homogeneous liquid of finite and infinite depth due to an arbitrary oscillating source situated at a finite depth below the undisturbed free surface of the liquid. The initial value problem is solved by using Laplace-Fourier transforms combined with asymptotic methods. The asymptotic solution is found to consist of the steady state and the transient components which are independently modified by surface tension. The latter decays more rapidly as timet due to the presence of surface tension than in the case where surface tension is neglected. It is predicted that the principal effect of surface tension is to increase both the phase and group velocity of the waves and make the energy more readily available among the rapidly travelling progressive surface waves. In addition to the effects of surface tension on the physical properties of the wave motions, our method of solution provides an interesting illustration of the applicability of generalized functions in water wave phenomena.     

Wave-propagation in uniaxially-stressed elastic media

Summary The propagation of waves of small amplitude in an elastic medium, with a particular form of strain-energy function, and subjected to a large homogeneous uniaxial stress, is considered in detail. The main characteristics, including speed and polarisation, of these waves in an unbounded medium are calculated numerically, and the existence and general properties of Rayleigh waves on the surface of a semi-infinite medium are investigated.     

Wave propagation in two layered medium under initial stresses

Summary In this paper, the frequency equation for phase velocity of waves propagated in a laminated medium consisting of two eleastic layers of finite thickness under initial stresses, has been obtained. It has been shown that when wave length becomes very small compared to the thickness of each layer, the wave approaches two Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface. The propagation ofSH-waves in the composite medium under initial stresses has also been discussed. A particular case has been taken to find the velocity of Love wave in the homogeneous half space under initial compressive stresses.Biot's incremental deformation theory has been used.     

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.     

Torsional wave under initial stress

Summary In this paper, the frequency equation for phase velocity of torsional wave in a rod of circular cross section under initial tension has been obtained. The graphs are plotted to compare the velocity with that in the absence of initial tension. Some analytical informations have been obtained for instability of the body under initial compression.     

On magneto-elastic transverse surface waves in an initially stressed half-space

Summary Transverse waves in an electrically conducting initially stressed elastic half-space with stress free boundary permeated by a magnetic field are investigated. The conditions for the existence of these waves is obtained and the velocity as well as the depth of penetration is calculated. In the absence of the initial stresses our results reduce to already known results.     

伴随地震波动的一种磁扰

本文应用磁弹性波理论,提出伴随地震波传播的同时,地磁场将产生一个扰动。在电导率σ→∞的理想情况下,震源附近的磁场变化约几个伽玛的量级。对于有限电导率情况,这种磁扰仍然存在。     

Electromagnetic response of a covered inhomogeneous permeable conductor in time domain

Summary An initial value induction problem has been solved to examine the response of a massive sulphide ore body under conditions of common occurence. The generalized expression for the induced field due to a step-function dipolar field in the presence of a non-uniformly conducting permeable sphere surrounded by a finitely resistive overburden has been derived. Two cases, when the concentric shell is (i) insulated from and (ii) in galvanic contact with the inner core, have been considered. The analytical results are in computable form to yield the decay-characteristics for application in geoelectromagnetics. Particular cases of the problem treated by the other investigators are discussed.N.G.R.I. Contribution No. 71-234     

Propagation of plane waves in an unbounded elastic medium with Cauchy's initial stress

Summary Cauchy theory of initial stress has been applied to investigate the influence of uniform initial stress on the propagation of plane waves in an unbounded elastic medium. It is found that if the initial principal stresses are unequal, the velocity depends on the direction in which the wave propagates, whereas when the initial principal stresses are equal, the velocity is independent of the direction of wave propagation.