Wave finite element method for waveguides and periodic structures subjected to arbitrary loads

The wave finite element method has been developed for waveguides and periodic structures with advantages in the calculation time. However, this method cannot be applied easily if the structure is subjected to complex or density loads and this is the aim of this article. Based on the finite element method, the dynamic equation of one period of the structure is rewritten to obtain a relation between the responses (DOF and nodal loads) on the left and right boundaries. This relation presents an additive term which links to the loads applying on the period. Then, by using WFE technique, we can compute the wave modes of the period and the wave decomposition. Because of the periodicity, we can also obtain a relation between the response and the left and right ends of the structure. Afterwards, the responses of the structure are calculated by using the wave decomposition in the dynamic stiffness matrix (DSM) approach or the wave analysis (WA). For the DSM approach, this technique shows that the external loads have no contribution to the global matrix but they lead to an equivalent force in the dynamic equation. Meanwhile, the external loads create waves propagating to the left and right of the structure in the WA approach.