Wave transmission through two-dimensional structures by the hybrid FE/WFE approach

The knowledge of the wave transmission and reflection characteristics in connected two-dimensional structures provides the necessary background for many engineering prediction methodologies. Extensive efforts have previously been exerted to investigate the propagation of waves in two-dimensional periodic structures. This work focuses on the analysis of the wave propagation and the scattering properties of joined structures comprising of two or more plates. The joint is modelled using the finite element (FE) method whereas each (of the joined) plate(s) is modelled using the wave and finite element (WFE) method. This latter approach is based on post-processing a standard FE model of a small segment of the plate using periodic structure theory; the FE model of the segment can be obtained using any commercial/in-house FE package. Stating the equilibrium and continuity conditions at the interfaces and expressing the motion in the plates in terms of the waves in each plate yield the reflection and transmission matrices of the joint. These can then be used to obtain the response of the whole structure, as well as investigating the frequency and incidence dependence for the flow of power in the system.