Transient radiation in a plane stratified dispersive medium. I. Half-space configuration

1968 ◽  
Vol 46 (9) ◽  
pp. 1059-1071 ◽  
Author(s):  
Edward Ott ◽  
Jerry Shmoys
Keyword(s):  
Half Space ◽  
Dispersive Medium ◽  
Current Source ◽  
Closed Form Solution ◽  
Independent Solution ◽  
Delta Function ◽  
Form Solution ◽  
Space Problem ◽  
Magnetic Current ◽  
Similarity Principle

In this paper a similarity principle will be derived for a class of transient diffraction problems in cold, lossless, isotropic plane stratified plasmas. The similarity principle will be utilized to obtain an exact closed-form solution to the problem of a magnetic current source whose density is a delta function (in space and time) situated either in or above a homogeneous plasma half-space. This solution will be interpreted in terms of rays and group velocity. An independent solution to the half-space problem will also be obtained using asymptotic techniques. Exact and asymptotic solutions will be compared and discussed.

Transient Response of an Elastic Homogeneous Half-Space to Suddenly Applied Rectangular Loading

1994 ◽  
Vol 61 (2) ◽  
pp. 256-263 ◽  
Author(s):  
F. Guan ◽  
M. Novak
Keyword(s):  
Laplace Transform ◽  
Half Space ◽  
Transient Response ◽  
Integral Kernel ◽  
Closed Form Solution ◽  
Contact Problems ◽  
Form Solution ◽  
Inverse Laplace Transform ◽  
Line Load ◽  
Homogeneous Half Space

A closed-form solution of transient response to suddenly applied loading distributed over a rectangular area on the surface of an elastic homogeneous half-space is developed for special purposes such as analysis of dynamic soil-structure interaction or contact problems. The solution is obtained using Laplace transform with respect to time and Fourier transform with respect to space. Inverse Laplace transform is implemented analytically. As extreme cases of rectangular loading, the solutions for a point force or finite line load can also be obtained. The advantages of this solution over most other solutions by numerical analyses are that the multiple integrations are reduced by one order, the singularity is removed from the integral kernel, and no additional discretization in the vicinity of the region of interest is required.

scholarly journals New Poisson's Type Integral Formula for Thermoelastic Half-Space

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Victor Seremet ◽  
Guy Bonnet ◽  
Tatiana Speianu
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Mixed Boundary ◽  
Integral Formula ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Volume Dilatation ◽  
Type Integral

A new Green's function and a new Poisson's type integral formula for a boundary value problem (BVP) in thermoelasticity for a half-space with mixed boundary conditions are derived. The thermoelastic displacements are generated by a heat source, applied in the inner points of the half-space and by temperature, and prescribed on its boundary. All results are obtained in closed forms that are formulated in a special theorem. A closed form solution for a particular BVP of thermoelasticity for a half-space also is included. The main difficulties to obtain these results are in deriving of functions of influence of a unit concentrated force onto elastic volume dilatation and, also, in calculating of a volume integral of the product of function and Green's function in heat conduction. Using the proposed approach, it is possible to extend the obtained results not only for any canonical Cartesian domain, but also for any orthogonal one.

The Contact Problem for a Rigid Cylinder Pressed Between Two Elastic Layers

1977 ◽  
Vol 44 (1) ◽  
pp. 36-40 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Iterative Solution ◽  
Form Solution ◽  
Single Step ◽  
Space Problem ◽  
Rigid Cylinder ◽  
Elastic Layers ◽  
Layer Problem

The paper concerns the plane-strain problem of a rigid cylinder pressed between two identical elastic layers supported by rigid bases along which they may slide without friction. The essential difficulty of the problem is that there are three contact zones, one between the cylinder and the layers, and two, symmetrically placed, between the layers; the extent of these regions has first to be found. Alblas has given an iterative solution to the problem which reduces to a closed-form solution when the layers are half spaces. The purpose of the paper is to show that there is an elegant approximate solution of the half-space problem which is well suited to computation and which converges to the closed-form solution. The solution depends on some remarkable results obtained by extending the Chebyshev polynomials to the whole of the real line. The paper also provides a single-step approximate solution of the two-layer problem.

Exact closed-form solutions for Lamb’s problem—III: the case for buried source and receiver

2020 ◽  
Vol 224 (1) ◽  
pp. 517-532
Author(s):  
Xi Feng ◽  
Haiming Zhang
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Closed Form Solution ◽  
Time History ◽  
Natural Generalization ◽  
Elastic Half Space ◽  
Form Solution ◽  
Elementary Functions ◽  
Heaviside Step Function ◽  
Lamb’S Problem

SUMMARY In this paper, we derive the exact closed-form solution for the displacement in the interior of an elastic half-space due to a buried point force with Heaviside step function time history. It is referred to as the tensor Green’s function for the elastic wave equation in a uniform half-space, also a natural generalization of the classical 3-D Lamb’s problem, for which previous solutions have been restricted to the cases of either the source or the receiver or both are located on the free surface. Starting from the complex integral solutions of Johnson, we follow the similar procedures presented by Feng and Zhang to obtain the closed-form expressions in terms of elementary functions as well as elliptic integrals. Numerical results obtained from our closed-form expressions agree perfectly with those of Johnson, which validates our explicit formulae conclusively.

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