On the Use of Extended Plate Theories of Vekua–Amosov Type for Wave Dispersion Problems

The extended plate theory of I.N. Vekua – A.A. Amosov type is constructed on the background of the dimensional reduction approach and the Lagrangian variational formalism of analytical dynamics. The proposed theory allows one to obtain the hierarchy of refined plate models of different orders and to satisfy the boundary conditions on plates’ faces exactly by introducing the corresponding constraint equations into the Lagrangian model of two-dimensional continuum. The normal wave dispersion in an elastic layer is considered, the convergence of the two-dimensional solutions to the exact one is studied for the locking phase frequencies, the dimensionless stress distributions across the thickness of a layer are shown.