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.

Transient Motion of an Elastic Half Space Due to a Semi-Infinite Surface Line Load

1970 ◽  
Vol 37 (1) ◽  
pp. 205-207
Author(s):  
D. C. Gakenheimer
Keyword(s):  
Time Dependence ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Transient Solution ◽  
Line Load ◽  
Transient Motion ◽  
Infinite Line

A method is described for obtaining an exact transient solution to the problem of an elastic half space whose surface is excited by a semi-infinite line load. The load acts normal to the surface of the half space and it has impulsive time-dependence. The resulting displacement field is discussed.

Moving Load on a Plate Resting on an Elastic Half Space

1967 ◽  
Vol 34 (4) ◽  
pp. 910-914 ◽  
Author(s):  
J. D. Achenbach ◽  
S. P. Keshava ◽  
G. Herrmann
Keyword(s):  
Half Space ◽  
Moving Load ◽  
Elastic Half Space ◽  
Winkler Foundation ◽  
Bending Moments ◽  
Line Load ◽  
Resonance Effects ◽  
Small Load ◽  
Smooth Contact ◽  
Time Invariant

An elastic plate supported by a semi-infinite elastic continuum is subjected to a moving line load. Both welded and smooth contact between plate and foundation are considered. Dynamic solutions for the bending moments in the plate are presented that are time-invariant relative to a coordinate system moving with the load. Resonance effects at certain critical velocities are discussed. The response of the system depends significantly on the relative stiffness of plate and half space and on the type of contact. For the relatively stiff plate certain resonances occur for smooth contact but not for welded contact. For subcritical load velocities the bending moments are calculated and compared with corresponding bending moments for a plate on a Winkler foundation. The Winkler foundation is adequate for smooth contact and small load velocities.

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.

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