Abstract
The normal wave dispersion in functionally graded plates investigated by implying the hierarchical theory of plates−improving contribution to the Vekua-Amosov theory. The combined use of the Lagrangian formalism of the analytical dynamics of continuum, dimensional reduction method, and of the biorthogonal expansion technique allows one to obtain the hierarchical traditional, as well as semianalytical finite element models under the unified general variational formulation. The comparative analysis of the convergence of approximate solutions of the wave dispersion problem for the isotropic homogeneous plate is performed for the locking phase frequencies. The wave dispersion in power graded plates with symmetric through-thickness structure is considered, the convergence of solutions is analyzed for both orthogonal polynomial and finite element approximation, and the dependence of the locking frequencies on the power index is studied.
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