ABSTRACT
We describe the numerical-analytical method of accelerated convergence and the corresponding computational algorithm meant for constructing approximations of frequencies and shapes of free vibrations of a rectangular membrane with clamped boundary. The mass density of the membrane and its surface tension are described by functions which may change sharply and have a large variation. For definiteness, we describe calculations for the lowest vibration mode of a square membrane with constant surface tension and inhomogeneity of special type. The inhomogeneity is modelled by two orthogonal strips forming a cross or its modifications (shifted or asymmetrical cross, angle, T-shaped figure). The values of the density function (characterizing, in particular, the width of the strips and the position of their intersection) vary within a wide range. The membrane vibration characteristics are studied numerically and some interesting mechanical effects are detected and discussed.
