Abstract
This paper reports on the application of the geometric multiscale finite element method for the analysis of wave propagation in heterogeneous periodic solids. The proposed scheme exploits multi-node elements to describe the microstructure through a local, auxiliary mesh that resolves the fine scale features, and that is used to numerically compute a set of interpolation functions employed for elements formulations at the global level. The method is applied for the analysis of the dispersion properties of, and transient wave propagation in domains featuring periodicity in two dimensions. Band diagram calculations, wave velocities and time domain computations are conducted on solids discretized using two-dimensional and three-dimensional multiscale finite element meshes. Results for assemblies with periodic inclusions, phononic stubbed plates and structural lattices illustrate the effectiveness of the method. Accurate predictions of dispersion relations, wave modes and time domain simulations are obtained with significant reductions in model size. The presented examples also illustrate some of the interesting wave characteristics of the considered class of periodic structures, which include wave directionality and frequency bandgaps.
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