On the low- and mid-frequency forced response of elastic structures using wave finite elements with one-dimensional propagation

In this paper, the wave finite element (WFE) method is investigated for computing the low- and mid-frequency forced response of straight elastic structures. The method uses wave modes as representation basis. These are numerically calculated using the finite element model of a typical substructure with a small number of degrees of freedom, and invoking Bloch’s theorem. The resulting wave-based boundary value problem is presented and adapted so as to address Neumann-to-Dirichlet problems involving single as well as coupled structures. A regularization strategy is also presented. It improves the convergence of the WFE method when multi-layered systems are specifically dealt with. It employs an alternative form of the wave-based boundary value problem quite stable and easy to solve. The relevance of both classic and regularized WFE formalisms is discussed and numerically established compared with standard finite element solutions.