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International audienceIn 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

This paper presents a general formulation which addresses the issue of wave propagation in guided elastodynamic structures filled with acoustic fluid. The formulation is based on a finite element description of periodic systems. It leads to a general spectral problem, whose eigenvalues and eigenvectors are related to the free propagating wave properties. The formulation incorporates many simplified elastodynamic models of an analytical nature. Here, the formulation is stated for a fluid-structure guided medium. The free and forced frequency response of such elasto-acoustic system is fully formulated in the wave space. Reduction of the wave basis is discussed. Numerical simulations and comparisons with classic simplified theories clearly shows the pertinence of the proposed formulation. Moreover, it is clearly shown that, unlike most of the existing theories, the proposed formulation is not low frequency limited.

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