Flexural waves in metamatrerial beam with mechanical and electromechnical resonators

Abstract

In this paper, an elastic metamaterial beam model with mechanical and electromechanical resonators is proposed. The electromechanical resonator is composed of piezoelectric layers and shunt circuit, and the mechanical resonator is designed by high-static-low-dynamic stiffness (HSLDS), both of which can provide negative stiffness mechanism. Firstly, the fully coupled equations are established by using Hamiltonian principle. Secondly, under the assumption of an infinite number of resonators, the influence of resonator parameters on the bandgap characteristics is analyzed. In addition, the modal expansion method is employed to study the frequency response function of a cantilever beam with a finite number of resonators under the base excitation. The results show that the additional mass ratio, residual stiffness ratio and electromechanical coupling coefficient have great influence on the bandgap characteristics. Combining the mechanical and electromechanical resonators can effectively expand the bandgap ranges of the metamaterial beam. The locally resonant metamaterials with HSLDS and electromechanical resonators designed in this paper can obtain better bandgap characteristics and attenuation performance.