Vertical oscillations of a circular die on an elastic half-space with a cylindrical cavity

1993 ◽  
Vol 65 (3) ◽  
pp. 1629-1634 ◽  
Author(s):  
P. Ya. Malits ◽  
A. R. Snitser
Keyword(s):  
Half Space ◽  
Cylindrical Cavity ◽  
Elastic Half Space

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.

The propagation of waves in an elastic half-space containing a cylindrical cavity

1970 ◽  
Vol 67 (3) ◽  
pp. 689-710 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Half Space ◽  
Cylindrical Cavity ◽  
Elastic Half Space ◽  
System Of Equations ◽  
Expansion Theorem ◽  
Elastic Potentials ◽  
Time Harmonic ◽  
Propagation Of Waves ◽  
Radiation Conditions ◽  
Conditions At Infinity

AbstractThe problem of the propagation of time harmonic waves in an isotropic elastic half-space containing a submerged cylindrical cavity is solved analytically. Linear plane strain conditions are assumed. Using an expansion theorem proved in a previous paper (Gregory (3)), the elastic potentials are expanded in a series form which automatically satisfies the governing equations, the conditions of zero stress on the flat surface, and the radiation conditions at infinity. The conditions of prescribed normal and tangential stresses on the cavity walls are shown to lead to an infinite system of equations for the expansion coefficients. This system of equations is shown to be a regular L2-system of the second kind and from its unique l2-solution, the solution to the problem is constructed. The fundamental questions of existence and uniqueness are fully treated and methods are described for constructing the solution.Three applications of the general theory are presented dealing respectively with the production, amplification and reflexion of Rayleigh waves.

scholarly journals Dynamics of elastic half-space with cylindrical cavity supported by shell at axymmetrical loads

2017 ◽  
Vol 2017 (1) ◽  
pp. 91-99 ◽  
Author(s):  
V.I. Pozhuev ◽  
◽  
A.V. Fasolyak ◽  
Keyword(s):  
Half Space ◽  
Cylindrical Cavity ◽  
Elastic Half Space

Shrink fit of an elastic half-space with a cylindrical cavity

1995 ◽  
Vol 448 (1932) ◽  
pp. 81-88 ◽  
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elastic Half Space ◽  
Series Method ◽  
Dual Integral Equations ◽  
Axisymmetric Contact Problem ◽  
Shrink Fit

This paper deals with the axisymmetric contact problem for an elastic half-space with a cylindrical cavity when mixed boundary conditions are prescribed on the surface of the cavity. The problem is simplified to that of finding the solution of dual integral equations arising from the mixed boundary conditions. The solution is obtained by the series method, and quantities of physical interest are calculated.

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