SEMICLASSICAL THEORY OF FLEXURAL VIBRATIONS OF PLATES

We study the biharmonic equation of flexural vibrations of elastic pla tes by a semiclassical method that can easily be generalized for other models of wave propagation. Three terms of the asymptotic number of l evels for plates with smooth boundaries are derived and the trace form ula for the density of states is obtained. The main difference between this formula and the Gutzwiller trace formula for billiards is the ex istence of a specific phase factor obtained while reflecting from the boundary. Six hundred eigenvalues of a clamped stadium plate are obtai ned by a specially developed numerical algorithm and the trace formula is assessed, looking at its Fourier transform. An extra contribution occurs for a free plate due to the existence of boundary modes.