Vibration attenuation of metamaterial dual-beam with simultaneous acoustic black hole and local resonator

Abstract

In this work, a metamaterial dual-beam (MDB) structure with simultaneous acoustic black hole (ABH) and local resonator (LR) is proposed for achieving broadband vibration reduction effects in low frequency range. The MDB consists of periodically arranged dual-beam unit cells, with each unit cell comprising two upper wedge-shaped acoustic black hole beams, two lower wedge-shaped acoustic black hole beams, and spring-mass-spring resonators connecting the upper and lower beams. The dynamic stiffness matrix of the dual-beam is derived and calculated, followed by the calculation of the frequency response under initial excitation. The analysis reveals distinct local resonance band gaps and Bragg scattering band gaps in the frequency response. Finite element method simulations are conducted, showing good agreement between the frequency response curves and dispersion curves. Moreover, the coupling relationship between the local resonance band gaps and Bragg band gaps was investigated. In essence, significant vibration reduction effects in the ultra-low frequency range have been achieved. To study the effects of beam height, beam length, and spring stiffness on the band gaps, parameter analyses are conducted. Moreover, models of multi-span beams are examined, revealing ultra-low frequency band gaps starting from 0 Hz. This study offers guidance in dual-beam structures at broadband vibration reduction effects in low frequency range.