Multiple Diffractions of Elastic Shear Waves by a Rigid Rectangular Foundation Embedded in an Elastic Half Space

1976 ◽  
Vol 43 (2) ◽  
pp. 295-299 ◽  
Author(s):  
M. Dravinski ◽  
S. A. Thau
Keyword(s):  
Half Space ◽  
Equation Of Motion ◽  
Elastic Half Space ◽  
Embedment Depth ◽  
Sh Wave ◽  
Strain Type ◽  
Time Required ◽  
Elastic Shear ◽  
Base Width ◽  
Rectangular Foundation

A rigid rectangular foundation, embedded in an elastic half space, is subjected to a plane, transient, horizontally polarized shear (SH) wave. Embedment depth of the foundation and the angle of the incidence of the plane wave are assumed to be arbitrary. The problem considered is of the antiplane-strain type. The Laplace and Kontorovich-Lebedev transforms are employed to derive the equation of motion for the foundation during the period of time required for an SH-wave to traverse the base width of the obstacle twice. Therefore this solution includes the process of multiple diffractions at the corners of the foundation.

Multiple Diffractions of Elastic Waves by a Rigid Rectangular Foundation: Plane-Strain Model

1976 ◽  
Vol 43 (2) ◽  
pp. 291-294 ◽  
Author(s):  
M. Dravinski ◽  
S. A. Thau
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Elastic Waves ◽  
Equation Of Motion ◽  
Elastic Half Space ◽  
Strain Type ◽  
Time Required ◽  
Strain Model ◽  
Rectangular Foundation ◽  
Plane Strain Model

A rigid rectangular foundation embedded in an elastic half space moves in a direction perpendicular to the surface of the half space, Fig. 1. The model under consideration is of the plane-strain type. By application of the Laplace, Fourier, and Kontorovich-Lebedev (K-L) transforms, the equation of motion for the foundation is derived. The transient response of the foundation is exact during the period of time required for a longitudinal wave to traverse the base of the foundation twice. Thus the process of multiple diffractions at the corners of the foundation is taken into account.

Transient Response of a Buried Foundation to Antiplane Shear Waves

1973 ◽  
Vol 40 (4) ◽  
pp. 1061-1066 ◽  
Author(s):  
S. A. Thau ◽  
A. Umek
Keyword(s):  
Equation Of Motion ◽  
Elastic Half Space ◽  
Antiplane Shear ◽  
Initial Time ◽  
Earthquake Response ◽  
Sh Wave ◽  
Time Period ◽  
Long Time ◽  
Base Width ◽  
Rectangular Foundation

A rigid rectangular foundation, embedded at an arbitrary depth below the surface of an elastic half space is subjected to a plane, transient SH-wave. The Laplace and Kantorovich-Lebedev transforms are applied to derive the equation of motion for the foundation during the initial time period required for an SH-wave to traverse the base width. The peak impulse response is found to occur during this time and the response there-after appears to be valid based on a comparison with the known, long-time limit. Consequently, the results presented here can be convolved with an earthquake accelerogram to yield an accurate foundation earthquake response.

scholarly journals The SH wave scattering of a heterogeneous hill in an elastic half-space

2020 ◽  
Vol 22 (5) ◽  
pp. 1145-1164
Author(s):  
Wang Dai ◽  
Zhang Hai ◽  
Wu Di ◽  
He Ying
Keyword(s):  
Half Space ◽  
Wave Scattering ◽  
Elastic Half Space ◽  
Sh Wave

Transient Response of an Elastic Half Space Subjected to a Reciprocating Antiplane Shear Load

1976 ◽  
Vol 43 (4) ◽  
pp. 625-629 ◽  
Author(s):  
K. Watanabe
Keyword(s):  
Analytical Solution ◽  
Wave Front ◽  
Half Space ◽  
Wave Speed ◽  
Elastic Half Space ◽  
Trigonometric Function ◽  
Antiplane Shear ◽  
Maximum Speed ◽  
Shear Load ◽  
Sh Wave

In this paper we consider a problem of the response of an elastic half space subjected to an antiplane shear load. The load is suddenly applied and thereafter moves in an interval reciprocally as a trigonometric function of time. An analytical solution for the displacement is obtained in terms of single integration. It is shown that the discontinuity in the displacement occurs only for the case that the initial (maximum) speed of the load is greater than the speed of SH-wave. In this case the displacement has a finite jump on the leading wave front and a logarithmic discontinuity immediately behind the wave front which emanates from a point where the load speed comes up with SH-wave speed. Numerical calculations are carried out for several cases of the initial (maximum) speed of the load and are shown graphically.

SH-wave velocity in a fiber-reinforced anisotropic layer overlying a gravitational heterogeneous half-space

2015 ◽  
Vol 11 (3) ◽  
pp. 386-400 ◽  
Author(s):  
Rajneesh Kakar
Keyword(s):  
Dispersion Equation ◽  
Half Space ◽  
Love Wave ◽  
Elastic Half Space ◽  
Wave Number ◽  
Fiber Reinforced ◽  
Sh Wave ◽  
Dimensionless Wave Number ◽  
Sh Waves ◽  
Content Type

Purpose – The purpose of this paper is to investigate the existence of SH-waves in fiber-reinforced layer placed over a heterogeneous elastic half-space. Design/methodology/approach – The heterogeneity of the elastic half-space is caused by the exponential variations of density and rigidity. As a special case when both the layers are homogeneous, the derived equation is in agreement with the general equation of Love wave. Findings – Numerically, it is observed that the velocity of SH-waves decreases with the increase of heterogeneity and reinforced parameters. The dimensionless phase velocity of SH-waves increases with the decreases of dimensionless wave number and shown through figures. Originality/value – In this work, SH-wave in a fiber-reinforced anisotropic medium overlying a heterogeneous gravitational half-space has been investigated analytically and numerically. The dispersion equation for the propagation of SH-waves has been observed in terms of Whittaker function and its derivative of second degree order. It has been observed that on the removal of heterogeneity of half-space, and reinforced parameters of the layer, the derived dispersion equation reduces to Love wave dispersion equation thereby validates the solution of the problem. The equation of propagation of Love wave in fiber-reinforced medium over a heterogeneous half-space given by relevant authors is also reduced from the obtained dispersion relation under the considered geometry.

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