Solução analítica de um problema bidimensional de propagação de ondas em meio não homogêneo pelo método de separação de variáveis

Abstract

The research involved in this work presents an analytical methodology for the solution of an inhomogeneous dynamic problem by the Method of Separation of Variables. This initiative aims to contribute to the establishment of a database of analytical solutions that can serve to validate the responses of numerical methods when applied in different areas in the study of waves. It can be pointing out that the availability of analytical solutions concerning the branch of wave propagation in heterogeneous media is greatly reduced, thus requiring contributions that can validate with greater accuracy the results of various numerical techniques. The Method of Separation of Variables resolve some of these problems of great complexity by reducing the partial differential equations in a set of ordinary differential equations for each independent variable. Due to the complexity of the problem approached, special functions appear in modeling requiring sophisticated mathematical manipulation and the aid of a computer program that solves the algebrisms and more complex integrals. The solutions are given in terms of displacements approximated by a finite number of terms in a series consisting of special functions.