The methods of external and internal excitation for problems of free vibrations of non-homogeneous membranes

In this paper a new numerical technique for problems of free vibrations of non-homogeneous membranes: ∇2w+k2q(x)w=0,x∈Ω⊂R2,B[w]=0,x∈∂Ω is presented. The method is based on mathematically modelling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Two versions of the method are described. The results of the numerical experiments justifying the method are presented.