Thermo-elastic interactions in an infinite elastic solid due to a concentrated transient heat source

Summary The present paper is concerned with the determination of thermo-elastic stress and temperature distribution in an infinite elastic solid when it is subjected to a concentrated transient heat source taking into account the effect of coupling. The fundamental partial differential equation for the thermo-elastic potential is solved by means of the operational method. The solutions are obtained for small values of time in terms of known functions such as complementary error functions and associated complementary error functions and have the form of power series with respect to the parameter of coupling . Since this parameter is generally very small for most of the metals, the expressions for stress and temperature distribution have been obtained by considering terms upto linear .     

Steady state thermal stresses in an elastic layer

Summary In this paper, steady state thermoelastic stresses in an elastic layer when there is a heat flux at one of its bounding planes, have been determined by the method of differential operators and Mittag-Leffler theorem.     

Stresses and displacements due to a stationary point source of heat in an elastic halfspace

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On stresses and displacements due to a moving line load over the plane boundary of a heterogeneous elastic half-space

Summary The problem of concentrated line load moving with supersonic speed along the boundary of an isotropic heterogeneous medium has been solved as a plane strain problem. The stresses and displacements in the heterogeneous case considered are found to decay exponentially with distance.     

Dynamic stresses in an elastic half-space

This paper deals with the problem of time-varying point loads applied onto the surface of an elastic half-space and the stresses that such loads elicit within that medium. The emphasis is on the evaluation of the isobaric contours for all six of the stress components at various frequencies of engineering interest and for a full range of Poisson’s ratios. The extensive set of pressure bulbs presented herein may be of help in predicting the severity of dynamic effects in common practical situations in engineering—or even the lack thereof.     

The transient disturbance produced in an elastic layer by a buried spherical source

Summary In this paper approximate expressions for the surface displacements due to a buried spherical source inside an isotropic elastic layer with one surface stress-free and the other (i) rigid, (ii) stress-free, have been obtained. Graphical representations for the surface displacements at a large distance have also been found.     

Three-dimensional elastic wave scattering and diffraction due to a rigid cylinder embedded in an elastic medium by a point source

The formal solutions of displacement field to the problem of elastic wave scattering and diffraction due to an infinitely long rigid cylinder embedded in an infinite elastic medium by an impulsive point source have been obtained in the integral form. The integrals for the reflected and the diffracted waves both in the shadow zone and in the illuminated zone are evaluated asymptotically for the early time motion by the Reisdue-Cagniard method and the Saddle-point-Cagniard method.Numerical results of the diffractedP, S andPS waves at a fixed circum-distance from the surface of the rigid cylinder show noticeably that (1) the energy partition for the diffractedS wave is small in comparison with that for the diffractedP wave, (2) the wave form of the diffractedS wave is broader and more diffused than that of the diffractedP wave, (3) the direction of the radial motions of the diffractedP andS waves varies as a function of the observational point, and (4) the energy partition for the diffractedP wave is much smaller than that for the direct or the reflectedP waves.This paper has been presented at the 46th Annual International Meeting of Society of Exploration Geophysicists in Houston, Texas, Oct. 28, 1976.     

Love waves due to a point source in an axially symmetric heterogeneous layer between two homogeneous halfspaces

Summary Acoustic gravity waves, propagating over a spherical earth with an isothermal and windless atmosphere, are considered. The perturbed pressure is expressed as a sum of discrete modes which are shown to be orthogonal. It is found that the excitation for the modes is determined by the specified normal particle velocity over a conical surface enclosing the source. One of the modes excited is shown to have characteristics closely akin to a Lamb wave on a flat earth for an isothermal atmosphere.This work was carried out while the author was a visiting professor at Harvard University.     

On the two dimensional thermo-elastic waves due to the distribution of stresses produced by an impulsive heat nucleus

Summary In this two dimensional thermoelastic problem, the distribution of components of displacement and stress are determined in an infinite elastic solid when the time dependent body force and an impulsive heat nucleus act upon certain region of the solid.     

Waves and stresses produced in an elastic medium due to impulsive radial forces and twist on the surface of a spherical cavity

Summary Displacements and stresses produced by impulsive radial pressure and by impulsive twists have been determined. In the former case total flow of energy across a spherical boundary has been obtained.     

Generation of SH-type waves due to shearing stress discontinuity in a sandy layer overlying an isotropic and inhomogeneous elastic half-space

The generation of SH-type waves due to sudden application of a stress discontinuity which moves after creation at the sandy layer of finite thickness overlying an isotropic and inhomogeneous elastic half-space is considered. The displacements are obtained in exact form by the method due to Cagniard modified by De Hoop. The numerical calculations are obtained. Two cases of shearing stress discontinuities are considered for different sandiness parameters. The graphs are drawn to show the effect of sandiness in the displacement components.     

Diffraction of an arbitrary wave due to a half plane

Summary Diffraction problems of an arbitrary wave by a half plane is solved exactly with the help of the integral equation technic. The solution is made to depend on a simple real quadrature which readily evaluates in exact forms, for different complicated type of incident fields. The method is supposed to produce new results, some of which are placed in the paper. The problem of Sommer-feld's plane wave diffraction is also solved as a very simple special case.     

Waves produced in an infinite elastic medium due to normal forces and twists on the surface of a burried spherical source

Summary In this paper, the waves propagated in an infinite medium has been considered by disturbances on the surface of a burried spherical source. The disturbances are produced by two types of forces viz. i) Transient normal force, ii) Transient twist applied on the surface of the source. The solutions are obtained in a very simple form. Graphical representations of some numerical solutions has been added at the end of each problem.     

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.     

On the disturbance due to a spherical distortional pulse in an elastic medium

Summary Theoretical expressions are derived for the displacement, velocity and stress in the time domain induced by an axially symmetric shearing stress applied at the inner surface of a spherical cavity in a hornogeneous, isotropic, elastic medium of infinite extent. Theoretical seismograms are computed for a step source and for three sources with exponential decay in time. A satisfactory time-dependence of the source can be obtained by combining the step source with one or more exponentially decaying sources.     

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.     

On the disturbance due to a point source in an inhomogeneous medium

Summary The problem of a point source in an isotropic, inhomogeneous fluid medium is discussed. It is assumed that the density of the fluid is constant and the acoustic velocity varies with depth asc=c ₀(1 +m z) wherem is a constant andc ₀ is, the velocity at the level of the origin. An approximate expression for the field due to a point source in such a medium is obtained when the medium is infinite as well as when it is semi-infinite. It is found that the results obtained agree with the WKB solution of the problem.     

Peak surface motion due to scattering of plane harmonic P,SV, or Rayleigh waves by a rough cavity embedded in an elastic half-space

Scattering of plane harmonic P, SV, or Rayleigh waves by a two-dimensional rough cavity completely embedded in an isotropic elastic half-space is investigated by using a direct boundary integral equation method. The cavity’s roughness is assumed to be in the form of periodic or random perturbations of arbitrary amplitude superimposed to a smooth elliptical shape. For the randomly corrugated cavities the normal or the uniform probability distribution functions are assumed. Based on multiple random cavity results, the corresponding average surface response is computed. These are compared with the corresponding periodically corrugated and smooth cavity responses. The surface response is evaluated for different cavity shapes and incident waves and for a range of frequencies. The surface motion results are used to determine the peak surface motion frequencies. They depend strongly upon the basic inclusion shape (the principal axes) and the nature of the incident wave. Strong similarity in the peak surface motion frequencies can be observed for the rough and smooth cavity models for both circular and elliptical shapes. In order to quantify the importance of the cavity corrugation upon the surface motion, a roughness influence factor is defined in terms of the rough and smooth cavity surface responses. This factor strongly depends upon the type of the incident wave, the nature of the cavity corrugation, the basic cavity shape, and the frequency. The factor clearly shows the effect of the cavity roughness upon the surface motion.     

The disturbance due to a point source in a homogeneous liquid layer over a heterogeneous liquid half-space

Summary The problem of a periodic point source in a homogeneous liquid layer overlying a heterogeneous liquid half-space is discussed. After obtaining the formal solution, the path of integration for the displacement potential of the layer is transformed from the positive real axis to the positive imaginary axis and the Sommerfeld contour and the latter is further distorted to the modified Sommerfeld contour. The residues of the integrand at the poles contained within the Sommerfeld loop constitute the normal mode solution to the problem. The integrands in the expressions for the integrals along the imaginary axis are expanded in a series of negative powers of exponentials and then some of the terms in these expansions are evaluated approximately. This gives various waves reflected from the interface and the integral along the Sommerfeld loop vanishes. The frequency equation is obtained, also by the principle of constructive interference. An expression for the reflection coefficient at an interface of two liquid media, the upper medium being homogeneous and the lower one inhomogeneous, is obtained.     

Hydromagnetic flow due to a transient plane

Summary The electromagnetic equations of Maxwell as well as the equations of fluid dynamics have been used to investigate the hydromagnetic flow due to the transient motion of a plane. The expressions for the velocity and skin-friction have been derived for small values of time by using Laplace transform techniques.