We evaluated the performance of the classical and spectral finite elementmethod in the simulation of elastodynamic problems. We used as a qualitymeasure their ability to capture the actual dispersive behavior of thematerial. Four different materials are studied: a homogeneous non-dispersivematerial, a bilayer material, and composite materials consisting of an aluminummatrix and brass inclusions or voids. To obtain the dispersion properties,spatial periodicity is assumed so the analysis is conducted using Floquet-Blochprinciples. The effects in the dispersion properties of the lumping process forthe mass matrices resulting from the classical finite element method are alsoinvestigated, since that is a common practice when the problem is solved withexplicit time marching schemes. At high frequencies the predictions with thespectral technique exactly match the analytical dispersion curves, while theclassical method does not. This occurs even at the same computational demands.At low frequencies however, the results from both the classical (consistent ormass-lumped) and spectral finite element coincide with the analyticallydetermined curves. Surprisingly, at low frequencies even the results obtainedwith the artificial diagonal mass matrix from the classical technique exactlymatch the analytic dispersion curves.
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