On Aspects of Asymptotics for Plate Equations

In this paper some initial-boundary value problems for plate equations will be studied. These initial-boundary value problems can be regarded as simple models describing free oscillations of plates on elastic foundations or of plates to which elastic springs are attached on the boundary. It is assumed that the foundations and springs have a different behavior for compression and for extension. An approximation for the solution of the initial-boundary value problem will be constructed by using a two-timescales perturbation method. For specific parameter values it turns out that complicated internal resonances occur.