Steady-state harmonic antiplane vibrations of a two-layer elastic half-space with a cylindrical cavity

1987 ◽  
Vol 27 (4) ◽  
pp. 595-599
Author(s):  
S. O. Vorob'eva ◽  
A. A. Lyapin ◽  
M. G. Seleznev
Keyword(s):  
Steady State ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Elastic Half Space

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.

scholarly journals Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity

2011 ◽  
Vol 18 (6) ◽  
pp. 827-838 ◽  
Author(s):  
İ. Coşkun ◽  
H. Engin ◽  
A. Özmutlu
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Circular Cross Section ◽  
Elastic Half Space ◽  
Least Square ◽  
Polar Coordinates ◽  
Wave Number ◽  
Forcing Function

The dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inner surface. The problem considered is one of plain strain, in which it is assumed that the geometry and material properties of the medium and the forcing function are constant along the axis of the cavity. The equations of motion are reduced to two wave equations in polar coordinates with the use of Helmholtz potentials. The method of wave function expansion is used to construct the displacement fields in terms of the potentials. The boundary conditions at the surface of the cavity are satisfied exactly, and they are satisfied approximately at the free surface of the half-space. Thus, the unknown coefficients in the expansions are obtained from the treatment of boundary conditions using a collocation least-square scheme. Numerical results, which are presented in the figures, show that the wave number (i.e., the frequency) and depth of the cavity significantly affect the displacement and stress.

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.

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