Governing Equations

Abstract

In this chapter fundamental governing equations for propagation of a harmonic disturbance on the surface of an elastic half-space is presented. The elastic media is assumed to be isotropic, continuous and infinite. Although this subject has been treated in various approaches in a number of references, it may be appropriate to develop a general procedure for solution of a number of essential soil dynamic problems based on the first principles of elasticity. The main scope of this chapter is to present a general systematic solution for addressing the problems considered in the next two chapters. This general solution is presented in two-dimensional Fourier domain in terms of elastic dilatation, and two elastic rotation components, which are used for decoupling of the involved partial differential equations. This chapter is also presenting the required fundamental of elasto-dynamics to achieve the set goal for the chapter.