Transverse vibrations of composite membranes of arbitrary boundary shape

This paper deals with an approximate method based on the technique of conformal mapping and a variational formulation which allows for a straightforward solution of the title problem for a certain type of composite membranes. Numerical results are presented for membranes of regular polygonal shape whose inner circular core possesses a density ρ 1 while the remaining is characterized by ρ 2. The fundamental eigenvalues are also verified by the Fourier expansion-collocation method and by a finite element algorithm.