The transient response of bonded piezoelectric and elastic half space with multiple interfacial collinear cracks

2002 ◽  
Vol 159 (1-4) ◽  
pp. 11-27 ◽  
Author(s):  
X. Zhao ◽  
S. A. Meguid ◽  
K. M. Liew
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Elastic Half Space ◽  
Collinear Cracks

Exact Transient Response of an Elastic Half Space Loaded Over a Rectangular Region of Its Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 516-522 ◽  
Author(s):  
F. R. Norwood
Keyword(s):  
Half Space ◽  
Real Axis ◽  
Transient Response ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Impulsive Loading ◽  
Rectangular Region ◽  
The Real ◽  
Algebraic Expressions ◽  
Straight Lines

The response of an elastic half space to a normal impulsive loading over one half and also over one quarter of its bounding surface is considered. By a simple superposition the solution is obtained for a half space loaded on a finite rectangular region. In each case the solution was found to be a superposition of plane waves directly under the load, plus waves emanating from bounding straight lines and the corners of the loaded region. The solution was found by Cagniard’s technique and by extending the real transformation of de Hoop to double Fourier integrals with singularities on the real axis of the transform variables. Velocities in the interior of the half space are given for arbitrary values of Poisson’s ratio in terms of single integrals and algebraic expressions.

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.

Response of an Elastic Half Space to Impulsive Stationary Finite Line Sources

1971 ◽  
Vol 38 (2) ◽  
pp. 549-550 ◽  
Author(s):  
F. R. Norwood
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Elastic Half Space ◽  
Line Load ◽  
Finite Line ◽  
Infinite Line

This Note considers the transient response in the interior of a half space acted upon by a normal impulsive stationary semi-infinite line load. The solution for the corresponding infinite line load problem is contained in the solution for the case of a semi-infinite line load. By a simple superposition, the solution is obtained for a half space acted upon by a finite line load.

scholarly journals Transient Response of an Elastic Half Space to Moving Loads

1981 ◽  
Vol 24 (192) ◽  
pp. 913-919 ◽  
Author(s):  
Kazumi WATANABE
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Elastic Half Space ◽  
Moving Loads

A Method for the Analysis of Transient Motion of a Kelvin-Voigt Half-Space

2003 ◽  
Vol 19 (1) ◽  
pp. 247-256 ◽  
Author(s):  
Chau-Shioung Yeh ◽  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Wen-Shinn Shuy
Keyword(s):  
Exact Solution ◽  
Half Space ◽  
Transient Response ◽  
Line Source ◽  
Elastic Half Space ◽  
Steepest Descent ◽  
Transient Motion ◽  
Modified Method ◽  
Causal Condition ◽  
Method Of Steepest Descent

ABSTRACTIn this paper, a modified version of method of steepest descent combining with Durbin's method is proposed to study the transient motion in either an elastic or a viscoelastic half-space. The causal condition is satisfied based on the Durbin's method while the wavenumber integral for any range of frequency is evaluated by applying the modified method of steepest descent. The validity and accuracy of the proposed method is tested by studying the transient response generated by a buried dilatational line source in an elastic half-space, for which the exact solution (Garvin's solution) can be obtained. Then the same formalism is extended to Kelvin-Voigt half-space, and the transient surface motions in elastic or viscoelastic half-spaces media are studied and discussed in details.

Sign in / Sign up

Export Citation Format

Share Document