Numerical experiments on the determination of eigenvalues in domains of complicated boundary shape

Originally printed-circuits boards have been of rectangular shape supported around the edges either continously or at a discrete set of points. However, increasing demands on electronics applications generate needs for more complicated shapes, Obviously the first step towards avoiding resonant mechanical conditions which in general lead to malfunction of the system is determining the frequency at which the plate resonates. Complicated boundary shapes are commonly used in microwave theory since rectangular and circular hollow waveguides do not meet optimum requirements from a practical viewpoint. The present paper deals with the performance of several numerical experiments on the determination of natural frequencies of vibrating plates and lowest cut-off frequencies of doubly connected hollow-piped waveguides.