`Shock and VibrationVolume 18, Issue 6, Pages 827-838http://dx.doi.org/10.3233/SAV-2010-0602`

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

İ. Coşkun,1 H. Engin,2 and A. Özmutlu3

1Faculty of Civil Engineering, Yıldız Technical University, Davutpaşa Campus, 34210 Esenler, Istanbul, Turkey
2Faculty of Civil Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey
3Department of Civil Engineering, Trakya University, 2250 Karaa&gbreve;aç, Edirne, Turkey

Received 8 February 2010; Revised 2 June 2010

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.