Low-frequency vibration insulation performance of the pyramidal lattice sandwich metamaterial beam

Abstract

A novel pyramidal truss core metamaterial beam with embedded internal mass-spring resonators is designed and its superior low-frequency vibration insulation performance is investigated. The infinite pyramidal truss core beam is modeled by Timoshenko beam model and the dispersion analysis is conducted to predict the bounds of the bandgap. For a finite pyramidal truss core metamaterial beam with specific boundary conditions, frequency responses of the structure are obtained numerically and experimentally to show the bandgap behavior. The results obtained by the three methods are consistent with each other. From the results, it is seen that the location and width of the bandgap can be selected by tailoring the natural frequency of the resonators, the inclination angle of the truss and the mass ratio of the resonators and face sheets. More numerical examples are further analyzed and it is found that the pyramidal truss core metamaterial beam with multi-frequency resonators can achieve much broader bandgaps than that with only a single array of resonators, although the two systems have the same host beam structure, lattice constant and total resonator masses in each unit cell.