Vibration Analysis of Continuous Bodies with the Use of Analytic Solutions Discretized on Boundaries. A Basic Study on Two-Dimensional Problems Described by Helmholtz's Equation.

Abstract

This paper discusses a new method of analysis of two-dimensional eigenvalue problems de-scribed by Helmholtz's equation. A general solution is assumed as a linear combination of plane waves which have the same wave number and travel in different directions. Nodal points are located only on the boundary of a convex domain which has an arbitrary shape. A set of equations similar to finite element equations can be derived from the general solutions. Eigenvalues obtained by this method are very close to the exact values. This method is effective in simplification of programming and in shortening of computational time.