Vibrations of a rectangular membrane with an eccentric inner circular boundary: A comparison of approximate methods

Three different approaches are used in order to obtain, independently, fundamental eigenvalues of the mechanical system under study: the Ritz method, the finite element algorithm and a Fourier expansion-collocation scheme. The agreement can be considered as very reasonable, especially in view of the relatively simple formulation of the Ritz approach in which two polynomial co-ordinate functions are employed. The results may also be of interest to acousticians and microwave specialists since they are applicable to soft-walled acoustical waveguides and TM modes in electromagnetic waveguides.