Principal and second instability regions of shear-deformable polygonal plates (Q1586899)

It is well known that initially flat plates under the action of time-periodic in-plane forces, if certain conditions concerning natural and exciting frequencies are fulfilled, may undergo a parametric instability. The authors extend existing studies to plates with arbitrary polygonal shape. Moreover, they include in their plate model the effects of rotatory inertia, shear and a two-parameter foundation. The derived set of partial differential equations is reduced by Galerkin method, using eigenfunctions as ansatzfunctions, to a set of Mathieu type equations describing the parametrically excited transversal plate vibrations. Numerical results are presented for simply supported plates on a two-parameter Pasternak-type foundation. The authors give boundaries of the first two instability regions. It is also shown that the special polygonal shape of the plate enters the formulation by means of eigenvalues of Helmholtz equation with homogeneous Dirichlet boundary conditions.