DYNAMIC ANALYSIS OF PERIODIC STRUCTURES AND METAMATERIALS VIA WAVE APPROACHES AND FINITE ELEMENT PROCEDURES

Two kinds of numerical approaches able to predict the dynamic response of periodic structures and metamaterials are presented. Both of them are model reduction techniques which can be used to obtain the response functions of the structures at a low computational cost. The first kind of approaches employs the wave finite element (WFE) method for modeling 1D periodic structures made up of complex substructures, e.g., 2D cells of arbitrary shapes. Resonant metamaterials are particular cases of periodic structures where the substructures possess local resonances — e.g., layered substructures involving soft layers and heavy layers/core —, which in turn lead to band gap effects and low vibration levels. Although well-suited for modeling periodic structures in the frequency domain, the WFE method also works for periodic structures subject to time-dependent excitations. The second kind of approaches employs finite element (FE) procedures for modeling 2D periodic structures, and 2D nearly periodic structures involving substructures with slightly varying (random) geometrical properties. For nearly periodic structures like plates with disordered resonant 2D cells, results show that the vibrational energy is localized around the excitation sources.