On the free vibrations of a rectangular plate with two opposite sides simply supported and the other sides attached to linear springs

In this paper an initial-boundary value problem for a plate equation will be studied. This initial-boundary value problem can be regarded as a rather simple model describing free oscillations of a suspension bridge. The suspension bridge is modelled as a rectangular plate with two opposite sides simply supported and the other sides attached to linear springs. An adapted version of the method of separation of variables is used to find the eigenfrequencies for this plate configuration.