A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology

Thesis (M.Eng.) - Asian Institute of Technology, 1988

In this study, two and three dimensional harmonic vibrations of two homogeneous elastic semi-infinite media perfectly bonded together are presented with the goal of developing shape functions in the far field of multilayered spaces for an infinite boundary element algorithm. In two dimensional problems, the vibrations caused by axisymmetric and asymmetric forces, and an anti-plane concentrated moment are considered. Vibrations due to axisymmetric and asymmetric forces, and pure torsion are considered in three dimensional problems. General solutions for different vibrations are formulated by the techniques of Fourier transforms with respect to the horizontal Cartesian coordinate in two dimensional problems, and Hankel transforms with respect to the cylindrical radial coordinate in three dimensional problems. The solutions in the forms of infinite integrals are determined by means of the residue theorem of the complex variables using a proper pair of contours in the complex plane. The complete solution ls obtained in the form of a single surface wave commonly lrnown as the Stoneley wave and continuous spectra of body waves. The integrals involved are evaluated numerically by means of the Simpson's rule. It is found that the displacement body waves may be composed of the contributions from the shear and pressure waves. Attempts are made to approximate each continuous spectrum of body waves by a finite number of discrete waves. For vibrations due to axisymmetric forces in a two and a three dimensional example problems, a shape function for each of such discrete waves is obtained.