Harmonic vibrations of infinite medium including two circular cylindrical cavities

ABSTRACT Engineering buildings like underground tunnels and pipe lines buried in infinite or semi- infinite elastic medium are subjected to dynamic effects such as liquid and gas pressures, traffic loads, earthquake waves and explosive shock waves. So, it is important to know the displacements and stresses in structures caused by these effects for design purposes. In this study, the harmonic vibrations of a lineer elastic infinite medium which is made of different kinds of materials and includes two cylindrical cavities is investigated. Each cavity is subjected to a harmonic excitation which is applied parallel to the lengthwise direction. In the first part of the study, past studies on the similar topic and the method used in this study are given. In the second part, equations of motion for the plain strain and anti-plain strain cases are given. In the third part, the formulation of the problem is made and the solution method is explained. The equations for each of the medium are solved analitically, by using the Bessel-trigonometric series. The unknown constants appeared in the solutions are obtained from the boundary conditions written on the cavity surfaces and the interface of the medium. The boundary conditions on the interface can not be satisfied exactly as there are infinite number of points and the series truncated for a finite number. Using the Least-Squares Technique, these conditions are satisfied approximately. In the fourth part, the displacements and stresses obtained for various parameters are shown in the graphics. For obtaining the numerical results and the graphics, Matlab (version 6.1) is used. Keywords: Infinite medium, cylindirical cavity, anti-plane strain, Least-Squares Technique. vn