AXISYMMETRIC CHARGE DISTRIBUTIONS ON AN ELASTIC DIELECTRIC HALF SPACE

1998 ◽  
Vol 22 (4B) ◽  
pp. 485-499
Author(s):  
K.L. Chowdhury
Keyword(s):  
Free Surface ◽  
Boundary Value Problem ◽  
Charge Distribution ◽  
Half Space ◽  
Fundamental Solutions ◽  
Potential Fields ◽  
Point Dipole ◽  
Charge Distributions ◽  
Electric Charge Distribution ◽  
Elastic Dielectric

The solution of the axisymmetric boundary value problem of an isotropic elastic dielectric half space subjected to charge distribution on its rigid polarization free surface is constructed by Hankel transforms. For the problem of an electric point dipole applied at origin, exact expressions for the components of displacement and polarization vectors and the potential fields are obtained in terms of Bessel function and fundamental solutions 1/R and e-mR/R, R being the distance from the source point. The electric field is determined both inside and outside the polarized region. In the particular case of a continuous electric charge distribution with density of the form l/(r2+h2)1/2, the mechanical and electric stresses on the surface of the semi-space are derived. The MathematicsTM software is used to present the numerical results on graphs depicting the variation of surface stresses for the particular charge distributions.

An expansion theorem applicable to problems of wave propagation in an elastic half-space containing a cavity

1967 ◽  
Vol 63 (4) ◽  
pp. 1341-1367 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Radiation Condition ◽  
Elastic Half Space ◽  
Potential Fields ◽  
Governing Equations ◽  
Expansion Theorem ◽  
Surface Conditions ◽  
Harmonic Vibrations ◽  
Time Harmonic

AbstractThis paper is principally concerned with the two-dimensional time harmonic vibrations of an elastic half-space y ≥ 0, containing a submerged cavity in the form of an infinite circular cylinder. Two sequences of line source potentials are obtained which are singular along the axis of the cylinder, satisfy the free surface conditions on y = 0, and represent outgoing waves at infinity. (The radiation condition.) It is proved that any solution of the governing equations which satisfies the free surface conditions and consists of outgoing waves at infinity is expansible as a sum of these fundamental source potentials, with coefficients to be determined from the boundary conditions on the cylinder only.The requirement of outgoing waves is carefully discussed and it is shown that the conditions taken give rise to, and are satisfied by, potential fields which would be regarded intuitively as representing outgoing waves.

scholarly journals The normal vibrations of a rigid spherical punch on the surface of an elastic half-space

1967 ◽  
Vol 15 (4) ◽  
pp. 297-307 ◽  
Author(s):  
R. J. M. Crozier ◽  
S. C. Hunter
Keyword(s):  
Free Surface ◽  
Boundary Value Problem ◽  
Half Space ◽  
Elastic Half Space ◽  
Contact Radius ◽  
Classical Elasticity ◽  
Total Load ◽  
Normal Vibrations ◽  
Image Position ◽  
Fixed Boundaries

SummaryA rigid spherical punch vibrates normally on the surface of a semi-infinite isotropic elastic half-space. The essential novelty of this problem, which is treated within the context of classical elasticity, is that of a changing boundary; the radius of the circle of contact on the free surface varies with time. The geometrical co-ordinates are modified to yield a boundary value problem with fixed boundaries. However the governing differential equations become more complicated. These equations are solved by a perturbation procedure for the case where the contact radius a(t) is of the formwhere a0 is constant and |ŋ(t)≪1. Finally the normal stress and the total load under the punch are evaluated in the form of series which are valid for sufficiently slowly varying ŋ(t).

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

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