Flexural wave attenuation by metamaterial beam with compliant quasi-zero-stiffness resonators

A novel metamaterial beam with embedded quasi-zero-stiffness (QZS) resonator is proposed to realize wave attenuation in very low-frequency band gaps. The configuration of the QZS resonator is developed by using compliant mechanism with design optimization, and the feature of quasi zero stiffness is achieved under proper pre-compression. Then, the dispersion relations of the metamaterial beam are derived by the transfer matrix method (TMM) to predicate the band gap theoretically. Additionally, the dynamic responses of the metamaterial beam are obtained by the spectral element method (SEM) to evaluate the transmittance of the flexural wave. Finally, the prototype of the metamaterial beam is fabricated by additive manufacturing, and the experimental investigation is conducted to verify the formation mechanism of the band gaps, which shows very low-frequency band gaps. Therefore, the QZS metamaterial beam should be promising in for low wave attenuation.

Automated summary

This paper proposes a novel metamaterial beam with an embedded quasi-zero-stiffness resonator to achieve wave attenuation in very low-frequency band gaps. The configuration of the quasi-zero-stiffness resonator is developed using compliant mechanism with design optimization, and the characteristic of quasi zero stiffness is achieved by proper pre-compression. The dispersion relations of the metamaterial beam are derived using the transfer matrix method, and the dynamic responses of the beam are obtained using the spectral element method to evaluate the transmittance of the flexural wave. Experimental investigation verifies the formation mechanism of the band gaps, demonstrating very low-frequency band gaps. Therefore, the QZS metamaterial beam holds promise for low wave attenuation.