scholarly journals Fundamental solutions for steady state dynamic problems in an elastic half-space and a consideration on their applicability.

1984 ◽  
pp. 363-366
Author(s):  
Tomiya TAKATANI ◽  
Yasutoshi KITAMURA ◽  
Shunsuke SAKURAI
Keyword(s):  
Steady State ◽  
Half Space ◽  
Fundamental Solutions ◽  
Elastic Half Space ◽  
Dynamic Problems ◽  
State Dynamic

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.

The Dynamic Response of an Elastic Half Space With an Overlying Acoustic Fluid

1976 ◽  
Vol 43 (1) ◽  
pp. 39-42 ◽  
Author(s):  
B. E. Bennett ◽  
G. Herrmann
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Elastic Solid ◽  
Elastic Half Space ◽  
Plane Interface ◽  
Dynamic Problems ◽  
Normal Loading ◽  
The Past ◽  
Method Of Solution ◽  
Acoustic Fluid

A class of dynamic problems involving a semi-infinite elastic solid with an overlying semi-infinite acoustic fluid, subjected at the plane interface to arbitrary normal loading is investigated. A method of solution is proposed which reduces the class of problems under study to that in which the fluid is absent. This latter class has received considerable consideration in the past. A specific example is presented for an expanding disk-shaped load including numerical results for the subseismic range.

Coupled Rocking and Lateral Vibrations of Embedded Footings

1973 ◽  
Vol 10 (2) ◽  
pp. 145-160 ◽  
Author(s):  
C. M. Urlich ◽  
R. L. Kuhlemeyer
Keyword(s):  
Steady State ◽  
Numerical Model ◽  
Half Space ◽  
Good Accuracy ◽  
Elastic Half Space ◽  
Spring Constant ◽  
Lateral Vibrations

A numerical model is described that was utilized to solve the problem of steady state coupled rocking and lateral vibrations of footings embedded into an elastic half space. The good accuracy of the model is confirmed by comparing results obtained for footings founded on the surface of the half space with corresponding results obtained by Veletsos and Wei (J. Soil Mech. Found. Div. Am. Soc. Civ. Eng. 97, pp. 1227–1249, 1971). The results indicate that embedded footings behave dynamically in a manner that cannot be properly predicted by the use of an appropriate embedded footing static spring constant in conjunction with displacement functions obtained for surface footings.

Transient fundamental solutions for a transversely isotropic elastic half space

1993 ◽  
Vol 442 (1916) ◽  
pp. 505-531 ◽  
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Fundamental Solutions ◽  
Elastic Half Space ◽  
Kernel Functions ◽  
Two Dimensional

This paper is concerned with the study of transient response of a transversely isotropic elastic half-space under internal loadings and displacement discontinuities. Governing equations corresponding to two-dimensional and three-dimensional transient wave propagation problems are solved by using Laplace–Fourier integral transforms and Laplace−Hankel integral transforms, respectively. Explicit general solutions for displacements and stresses are presented. Thereafter boundary-value problems corresponding to internal transient loadings and transient displacement discontinuities are solved for both two-dimensional and three-dimensional problems. Explicit analytical solutions for displacements and stresses corresponding to internal loadings and displacement discontinuities are presented. Solutions corresponding to arbitrary loadings and displacement discontinuities can be obtained through the application of standard analytical procedures such as integration and Fourier expansion to the fundamental solutions presented in this article. It is shown that the transient response of a medium can be accurately computed by using a combination of numerical quadrature and a numerical Laplace inversion technique for the evaluation of integrals appearing in the analytical solutions. Comparisons with existing transient solutions for isotropic materials are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses due to a buried circular patch load are presented to portray some features of the response of a transversely isotropic elastic half-space. The fundamental solutions presented in this paper can be used in the analysis of a variety of transient problems encountered in disciplines such as seismology, earthquake engineering, etc. In addition these fundamental solutions appear as the kernel functions in the boundary integral equation method and in the displacement discontinuity method.

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