Investigation and assessment of the wave and finite element method for structural waveguides

This dissertation concerns the Wave and Finite Element Method, applied to one- and two-dimensional periodic structures for the analysis of the wave propagation and the forced response. This method is appealing in the mid-frequency range, where FE models have a large number of degrees of freedom and the SEA provides approximated results. Within the WFE approach, a single elementary cell is modelled by using conventional Finite Elements. Mass and stiffness finite element matrices are then post-processed by applying periodicity conditions, in order to define a dynamic stiffness matrix which relates nodal DOFs and forces on the cell sides. This leads to the formulation of an eigenproblem, whose solutions are the waves' propagation constants, from which dispersion curves are obtained. Furthermore, from the dispersion relations, it is possible to estimate the forced response of a finite structure by applying the wave propagation approach. In this work, the elementary cell of a generic waveguide is modelled through Finite Elements. The mass and stiffness matrices are then post-processed in own codes. One-dimensional waveguides with different cross-sections are investigated, comparing the dispersion curves with analytical, full-FEA and literature ones. Furthermore, the forced response of composite and sandwich beams is carried out through the wave propagation approach. A first approach to the wave analysis of two-dimensional waveguides is also introduced, in order to validate experimental tests conducted on a natural fibres composite panel.