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.
