Internally coupled piezoelectric metamaterial beam with multi-functionalities

Abstract

A piezoelectric metamaterial beam is proposed in this paper for both vibration suppression and energy harvesting. Additional springs are introduced to create internal coupling alternately between local resonators. Each resonator is associated with a piezoelectric element for producing electrical energy. First, the mathematical model of the piezoelectric metamaterial beam is developed. The analytical solutions of the transmittance of the system and the open-circuit voltage responses of the piezoelectric elements are derived. As compared to the conventional counterpart without internal coupling, it is found that the energy harvesting performance is significantly reinforced in the low frequency range and the vibration suppression performance is slightly enhanced due to the appearance of an additional band gap. Subsequently, an equivalent finite element model – model A for verifying analytical solutions is developed. The lumped local resonators in the analytical model are modelled by using cantilevers with tip masses in the finite element model. The tip masses are alternately coupled with one-dimensional two-node spring elements. The finite element analysis results show good agreement with the analytical results for both the transmittance of the system and the open-circuit voltage responses of the piezoelectric elements. Finally, a model B with a more practical realization of the internal coupling is established. The coupling spring is replaced by a beam connection. The finite element analysis results show that the behavior of model B is different from model A and is not equivalent to the proposed analytical model. No significant enhancement in terms of energy harvesting is observed but a remarkably enhanced vibration suppression performance appears in model B. The difference between the two models is then discussed.