Showing papers on "Half-space published in 1977"

The forced two dimensional oscillations of a rigid strip in smooth contact with a semi-infinite elastic solid

Abstract: In this paper we investigate a time harmonic plane strain problem in a homogeneous isotropic semi-infinite elastic solid with mixed boundary conditions on its surface. The boundary is free from applied stress apart from on an infinite strip where the tangential components of stress are zero, and the normal component of displacement is a prescribed function. By reducing the mixed boundary value problem to the solution of a Fredholm integral equation of the second kind, an existence theorem is proved and a simple low frequency asymptotic formula relating the normal stress to the prescribed displacement is derived rigorously. The results are applied to the forced heaving and rocking motion of a rigid cylindrical body in smooth contact with an elastic half space. Some further applications to scattering problems are suggested.

Influence of motion of radiating particles on the concentration distribution at the boundary of a flat, semi-infinite layer

Abstract: The distribution of excited atoms near the surface limiting the half space has been determined. The transfer of the excited state by two mechanisms, absorption and reradiation of photons and space motion, has been taken into account. An analytical solution has been found for the integral equation describing joint diffusion of the photons and particles. The concentration of excited atoms at the half-space boundary, determined after accounting for their space motion, may differ by orders of magnitude from the values obtained by solving the Biberman-Holstein equation.

Acoustic diffraction by an impedance covered half-plane

Abstract: Exact, closed form solutions for diffraction and backscattering by an edge whose surfaces exhibit arbitrary impedances were determined for the cases of a point source, a line source, and a plane wave. An integral method was devised that could account for the impedance boundary conditions. Since the solution is in a closed form, interpretation of the influence of the impedance covered half plane on the diffraction field is greatly faciliated. Specifically, the effect of each surface on the acoustic field dominates in the half space in which it faces. Though the effect of each surface extends into the opposite half space behind the barrier, this influence is very small and diminishes even more as the observer moves further behind the barrier. [Work supported by NAVSEA.]

Lamb's Problem for an Impulsive Line Load on a Laminated Composite.

Abstract: : The effective stiffness theory developed by Sun, Achenbach, and Herrmann is used to model a periodically laminated linearly elastic half space that is subjected to an impulsively applied line load. The laminations are parallel to the free surface. An approximate solution is constructed by approximating formal solutions (inversion integrals) near saddle points for low frequency and large distance from the source. Contributions include the responses of the body waves as well as the head and Rayleigh waves. Numerical results are presented in order to illustrate the differences between the dispersive and nondispersive solutions. (Author)

A spherical wave in a viscoelastic half-space

Abstract: The propagation of spherical waves in an isotropie elastic medium has been studied sufficiently completely (see, e.g., [1–4]). it is proved [5, 6] that in imperfect solid media, the formation and propagation of waves similar to waves in elastic media are possible. With the use of asymptotic transform inversion methods in [7] a problem of an internal point source in a viscoelastic medium was investigated. The problem of an explosion in rocks in a half-space was considered in [8]. A numerical Laplace transform inversion, proposed by Bellman, is presented in [9] for the study of the action of an explosive pulse on the surface of a spherical cavity in a viscoelastic medium of Voigt type. In the present study we investigate the propagation of a spherical wave formed from the action of a pulsed load on the internal surface of a spherical cavity in a viscoelastic half-space. The potentials of the waves propagating in the medium are constructed in the form of series in special functions. In order to realize viscoelasticity we use a correspondence method [10]. The transform inversion is carried out by means of a representation of the potentials in integral form and subsequent use of asymptotic methods for their calculation. Thus, it becomes possible to investigate the behavior of a medium near the wave fronts. The radial stress is calculated on the surface of the cavity.

Calculation of the surface motion of a layered half-space by the method of Laplace transform

Abstract: A new method is presented for calculating the surface response of a horizontally stratified system of N homogeneous, isotropic, linearly anelastic layers with radiation damping, when subjected to a normally incident plane wave of arbitrary profile. The method used is that of Laplace transform and contour integration. In the case N = 1, the radiation damping coefficient is found to be − [tanh −1 I 1 ]/ s 1 for an elastic layer (where I 1 is the impedance ratio between the layer and underlying bedrock and s 1 is the time thickness of the layer). A solution, valid for low input frequencies, is also found for the damping coefficients and damped natural frequencies when viscous damping is present in the layer. For N > 1, the damping coefficients and damped natural frequencies are calculated numerically from an N -term recurrence relation. The method may have computational advantages over some existing methods of solution.

Transverse Propagation of Transient Electromagnetic Waves in a Non-homogeneous Half-space

Abstract: The problem of a transient, transverse electromagnetic wave incident on a non-homogeneous half space is considered. Solutions are obtained by both the Laplace transform technique (LT) and the method of characteristics (MOC). The former method yields an infinite number of exact solutions in closed-form provided that the dielectric and permeability parameters are distributed as power laws in the spacial coordinate. A method for systematically generating these solutions is given. The method of characteristics, in numerical form, provides approximate solutions along the curved characteristics. Agreement between the two methods is excellent, except for a certain anomalous class of inhomogeneities. Finally, certain quasi-static solutions, involving a variety of inhomogeneities, are demonstrated.

Convex surfaces whose geodesics are planar

Abstract: It is shown that ifC is a convex surface, in euclidean space of dimension at least 3, having the property that all shortest paths onC between pairs of its points are planar, thenC is a sphere, a hyperplane or the boundary of an intersection of two half-spaces. No smoothness assumptions are made.