Frequency Dependent Mechanical Properties of Elastic Metamaterials with Locally Resonant Microstructures

Frequency dependent mechanical properties of elastic metamaterials with locally resonant microstructures were investigated. Due to the dynamic behavior of the microstructures, the mechanical properties of these elastic metamaterials, if represented by effective continuous media, would exhibit frequency dependent characteristics. This phenomenon was studied from the energy propagation point of view. Based on the monatomic mass lattice model, two band gap formation mechanisms were proposed. For each representative element, considering the time period when effective mass velocity increases from zero to maximum, if the kinetic energy requirement is beyond the capability of the external work of external spring, the monatomic lattice type band gap would be generated; if the kinetic energy requirement is negative, the two inner masses interaction type of band gap would be generated. This analytical solution was also verified by FE simulation. Following that, the band gap in diatomic mass-in-mass lattice systems was explained based on the proposed two formation mechanisms, and the passing band between the two band gaps generated by the single negative effective mass in diatomic mass-in-mass lattice systems was eliminated based on the analytical derivation and verified by the tone burst wave propagation using FE simulation. Further, the dynamic behavior of rods made of elastic metamaterials with frequency dependent properties was investigated. Based on the frequency dependent mass density and Young’s modulus for the effective continuum, it was found that the rod natural frequency distribution was changed and no natural resonance frequency in the band gap region of the corresponding metamaterial. Besides, the general wave amplitude transfer function was derived for wave propagation in layered structures, and the final transmitted wave amplitude of the layered metamaterial structure with decreasing density was obtained using Mathematical Induction method. Making use of the frequency dependent properties, the elastic phase-controlling metalayer was also analyzed. It was analytically and numerically demonstrated that, whether a normal incident longitudinal wave can propagate through the interface depends on whether the wave length is larger or shorter than the periodic length of the metalayer element. In addition, since the phase gradients are the same at both sides of metalayer, this type of elastic metalayer may serve as an energy absorption material. Finally, the wave attenuation characteristics of an elastic metamaterial composed of spherical rubber-encased alumina particle inclusions in an epoxy matrix was verified by numerical simulation and coil shaker based vibration test. Moreover, the dynamic behavior of free-free end rod made of the same elastic metamaterial was obtained by piezoelectric patches based vibration tests. It was found that the wave attenuation effect would increase with the number of inner resonators, and the rod natural frequencies would shift ahead when input frequency was close to band gap region