Application of Nth-Order Plate Theory to the Dispersion of Progressive Waves in a Heterogeneous Medium

The generalized theory of Nth-order plates is applied to the dispersion of progressive waves in a plane heterogeneous medium with large local gradients of the density and elastic modulus, simulating a structural defect. This approach is based on the spatial reduction of a three-dimensional model of the layer and finite basis functions of the thickness corresponding to semianalytical finite elements. The dispersion problem reduces to a generalized spectral problem for a pair of symmetric matrices. The convergence of the solution in terms of locking frequencies of the wave is considered.