Keywords: multi-layered systems, wave finite elements, dynamic substructuring, global wave modes, local wave modes.

In this paper, the forced response of multi-layered elastic waveguides is addressed. The formalism uses global wave modes as a projection basis. These global modes are numerically constructed from the local wave modes of the layers within the framework of the modified wave finite element (MWFE) method. The method uses a dynamic substructuring scheme which allows the dynamics of each layer cross-section to be projected onto a reduced local wave mode basis with appropriate dimensions. Especially when layer cross-sections exhibit multiscale behavior, the MWFE method solves a set of numerical issues associated with the standard wave finite element (WFE) techniques. Particularly, it allows the classic global wave motions to be correctly captured. The MWFE method constitutes an underlying efficient reduced model to predict the forced response of multi-layered systems. This is explained because the kinematic variables, especially the boundary conditions, are projected onto specific bases, containing physical wave motions, whose dimension is related to the cross-section dynamics. We apply the MWFE formulation to describe the forced response of multi-layered systems. The framework of the method is recalled first. We present and solve the Neumann to Dirichlet problem associated with the formulation. Numerical simulations involving a sandwich structure under axial and transverse loads are presented. WFE and MWFE solutions are compared with standard finite element simulations. Numerical simulations and comparisons with standard techniques show the pertinence of the MWFE model.

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