Use of the higher-order plate theory of I. N. Vekua type in problems of dynamics of heterogeneous plane waveguides

Abstract

The dynamics of elastic plane waveguides is studied on the basis of the extended formulation of the plate theory of N th order. The plate model is based on the Lagrangian formalism of analytical dynamics combined with the dimensional reduction approach and the biorthogonal expansion of the spatial distribution of the displacement. The boundary conditions shifted from the faces onto the base plane are interpreted as constraints for the variational formulation of two-dimensional plate models. The normal wave dispersion in plates is modelled, the convergence of the approximate solutions is studied using the known exact solution for a plane layer as a reference. The proposed plate theory is used to analyse the normal wave dispersion in power graded waveguides of both symmetric and asymmetric structures, the locking phase frequencies for various power indices are computed.