Local resonator with high-static-low-dynamic stiffness for lowering band gaps of flexural wave in beams

Abstract

Periodic structures are effective in attenuating waves in low frequency range at local resonance (LR) conditions, but it is still a challenge to achieve this in very low frequency range. The main original contribution of this paper is to further lower the band gaps of flexural wave propagation in LR beams by developing a new resonator with high-static-low-dynamic stiffness (HSLDS). The proposed resonator is designed by combining a vertical spring with two oblique springs that provide negative stiffness in the vertical direction, and thus the stiffness of the vertical spring can be counteracted effectively by the negative-stiffness (NS) mechanisms. The band structures of HSLDS-LR beams, obtained by the transfer matrix method and verified by numerical simulations, demonstrate that band gaps can be shifted to much lower frequency than that of conventional LR beams. Most importantly, the band gaps can be assigned to desired locations by adjusting only the stiffness of the oblique springs. For wave attenuation in HSLDS-LR beams with a finite length, a sufficient number of unit cells are required to achieve a good performance of attenuation.