The Fourier solution of the wave equation for a circular vibrating membrane is generalized to a star-like-shaped structure. We show that the classical solution can be used in this more general case, provided that a suitable change of variables in the spherical co-ordinate system is performed.@en

The interior and exterior Neumann problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so called ¿superformula¿ introduced by Gielis. A dedicated numerical procedure based on a computer algebra system is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to classical ones, are obtained. Computed results are found to be in good agreement with theoretical findings on Fourier series expansion presented by Carleson.@en