A Method for Numerical Analysis of Wave Propagation in an Elastic Half Space

The analytical studies of blast effects and earthquake, mechanical or traffic foundation vibrations are to consider them as wave propagation problems in an infinite solid. When the geometrical complications as structures on the foundation or openings are included, it is not possible to find closed form solutions and, therefore, only the numerical solutions are available. As a numerical method, finite element or finite difference method is useful. With these methods, only a finite number of nodal points can be considered, the numerical method can not be used the direct approximation of the infinite region. One of the methods through which an infinite system may be approximated by a finite system is to use a viscous boundary condition. In this study it was considered that a continuous state is between the free and the fixed conditions. So the infinite region was approximated as the average of a finite system with free boundary condition and a system with fixed boundary condition. The numerical results showed that the method of superposition is excellent in one dimensional problems and not so good in two dimensional problems.