Band gaps and dynamics of locally resonant meta-plate with stiffness adjustable low frequency resonator

Abstract

This paper presents the band gaps and dynamics of locally resonant meta-plate with stiffness micro-adjustable high static and low dynamic resonator, in which a Euler-buckled beam provides negative stiffness. The resonator is periodically installed on a thin plate through a threaded linkage. By changing the axial displacement of the buckled beam, the total stiffness of the resonator is adjusted. Through the static analysis, the critical axial compression required for the buckled beam to provide negative stiffness is discussed. With the help of classical thin plate theory, the dynamic equation of the system is obtained. The band gaps of the locally resonant meta-plate are calculated by employing the plane wave expansion method. Considering the simply supported boundary condition, dynamic responses of the finite size locally resonant plate are shown with the aid of numerical simulation. The effects of the axial compression of the buckled beam, the mass of resonator, the damping of oscillators and plates, and spring stiffness of the system on the band gap are analyzed in detail.