On mathematical and analytical methods for solving problems on vibrations of membranes and plates

Abstract

The problems about determination of the frequencies and forms of natural vibrations of plates and shells lead to the necessity of partial differential equations integration. The well-researched cases are those where it is possible to separate the variables. In particular, these include the vibrations of a rectangular plate hinged on opposite sides, umbrella and fan vibration of circular axisymmetric plates and vibrations of cylindrical shells, closed or hinged along generating curves. In this work, the vibration of a flat homogeneous membrane is investigated for the general case of boundary conditions.