A wave finite element‐based formulation for computing the forced response of structures involving rectangular flat shells

Abstract

International audienceThe harmonic forced response of structures involving several noncoplanar rectangular flat shells is investigated by using the Wave Finite Element method. Such flat shells are connected along parallel edges where external excitation sources as well as mechanical impedances are likely to occur. Also, they can be connected to one or several coupling elements whose shapes and dynamics can be complex. The dynamic behavior of the connected shells is described by means of numerical wave modes traveling towards and away from the coupling interfaces. Also, the coupling elements are modeled by using the conventional finite element (FE) method. A FE mesh tying procedure between shells having incompatible meshes is considered, which uses Lagrange multipliers for expressing the coupling conditions in wave-based form. A global wave-based matrix formulation is proposed for computing the amplitudes of the wave modes traveling along the shells. The resulting displacement solutions are obtained by using a wave mode expansion procedure. The accuracy of the wave-based matrix formulation is highlighted in comparison with the conventional FE method through three test cases of variable complexities. The relevance of the method for saving large CPU times is emphasized. Its efficiency is also highlighted in comparison with the component mode synthesis technique

New advances in the forced response computation of periodic structures using the wave finite element (WFE) method

“…(26) well conditioned (this interesting feature is emphasized in [13,14]). In condensed form, the matrix system (26) is expressed as AQ = F , where…”

“…The procedure has been proposed in [13] when Neumann and Dirichlet conditions are dealt with. The same strategy holds for arbitrary boundary conditions, e.g., surface impedances [14]. Such boundary conditions can be formulated as…”

“…µ ⋆ j = 1/µ j . It will be shown in Section 4 that the non-consideration of the analytic relations (14) and (11) is source of numerical ill-conditioning, which appears dramatic for describing the forced response of structures.…”

“…This is explained since wave-based matrix systems of small size -which relates the number of DOFs on the cross-section of waveguides only -are considered rather than the full FE models of the waveguides. The WFE method has proved to be relevant, compared to the FE method and the component mode synthesis technique, to describe the dynamic behavior of sophisticated structures (see [14]). …”

A Wave-Based Reduction Technique for the Dynamic Behavior of Periodic Structures

“…Actually, there exist two main WFE-based strategies to compute the forced response of periodic structures. These are labeled as dynamic stiffness matrix (DSM) approach and wave amplitudes (WA) approach, and respectively involve expressing the condensed dynamic stiffness matrix of a periodic structure in terms of wave modes [3], or the vectors of wave amplitudes of the right-going and left-going modes [4,7,8]. The feature of the WFE method is that it makes use of the FE model of one single substructure only, rather than considering the full FE model of a whole periodic structure.…”