A Novel Elastic Metamaterial with Multiple Resonators for Vibration Suppression

Abstract

In this paper, two models of elastic metamaterial containing one and two resonators are proposed to obtain the bandgaps with the aim of providing broadband vibration suppression. The model with one DOF is built by assembling several unite cells in which each unite cell consists of a rectangular frame as the base structure and a rack-and-pinion mechanism that is joined to the frame with a linear spring on both sides. In the second model with two DOF, a small mass is added while its center is attached to the center of the pinion on one side and the other side is connected to the rectangular frame via a linear spring. In the first mechanism, the pinion is considered as the single resonator, and in the 2DOF model, on the other hand, the pinion and small mass acted as multiple resonators. By obtaining the governing equations of motion for a single cell in each model, the dynamic behavior of two metastructures is thoroughly investigated. Therefore, the equations of motion for the two models are written in matrix form, and then, the dispersion relations are presented to analyze the influences of system parameters on the bandgaps’ starting/ending frequencies. Finally, two models are successfully compared and then numerically simulated via MATLAB-SIMULINK and MSC-ADAMS software. With the aid of closed-form expressions for starting/ending frequencies, the correlation between the system parameters and bandgap intervals can be readily recognized.