Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators

Abstract

The wave propagation and vibration transmission in metamaterial-based elastic rods with periodically attached multi-degree-of-freedom (MDOF) dynamic anti-resonant vibration isolator (DAVI) resonators are investigated. A methodology based on a combination of the transfer matrix (TM) method and the Bloch theorem is developed, yielding an explicit formulation for the complex band structure calculation. The bandgap behavior of the periodic structure arrayed with single-degree-of-freedom (SDOF) DAVI resonators and two-degree-of-freedom (2DOF) DAVI resonators are investigated, respectively. A comparative study indicates that the structure consisting of SDOF DAVI resonators periodically jointed on the metamaterial-based elastic rod can obtain an initial locally resonant band gap 500 Hz smaller than the one given in the published literature. The periodic structure containing 2DOF DAVI resonators has an advantage over the periodic structure with SDOF DAVI resonators in achieving two resonance band gaps. By analyzing the equivalent dynamic mass of a DAVI resonator, the underlying mechanism of achieving a lower initial locally resonant band gap by this periodic structure is revealed. The parameters of the 2DOF DAVI resonator are optimized to obtain the lowest band gap of the periodic structure. The numerical results show that, with the optimal 2DOF DAVI parameters, the periodic structure can generate a much lower initial locally resonant band gap compared with the case before the optimization.