Abstract
This paper presents a method for solving eigenvalue problems of various phenomena that are governed by the Helmholtz equation with an arbitrarily shaped outer boundary and a number of eccentric boundaries of arbitrary shape. In the analysis, the outer boundary condition is satisfied by means of the Fourier expansion collocation method using the exact solution of the equation of motion. To satisfy the inner boundary conditions, the point restraints are added to the equation of motion, and the inner boundary conditions are satisfied by making use of a point matching procedure. The equation for finding the eigenvalues are derived, and numerical calculations are carried out for cases of elliptical outer and inner boundaries and polygonal outer and inner boundaries.
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