The two-degree-of-freedom local resonance elastic metamaterial plate with broadband low-frequency bandgaps

Abstract

A theoretical model of a new type of two-degree-of-freedom local resonance mass-spring system with the resonator considering vertical and rotational vibration (the moment of inertia) is proposed to generate a negative effective mass over specific frequency ranges. Based on the theoretical analysis, a novel elastic metamaterial plate is designed. The flexural vibration band structures as well as the transmission spectrum of the metamaterial plate are investigated by using the finite element method. Subsequently, the formation mechanism of the band gaps is analyzed by studying the displacement field of the eigenmodes at the band gap edges. At last, the effects of the geometrical parameters on the flexural vibration band gaps (FVBGs) are studied and discussed in detail. The related results well confirm that the two-degree-of-freedom metamaterial shows negative mass density in two distinctive asymptotic regions, and the proposed elastic metamaterial plate has two FVBGs with the total width of 94.45 Hz below 200 Hz. The magnitude of torques introduced into the local resonance system can obviously affect the locations of the FVBGs. For the elastic metamaterial plate with thick local resonance lead plate and weak rubber is appropriate to obtain a lower gap, but the total width of the FVBGs becomes narrow. However, it does just the opposite for the condition with thin local resonance lead plate and strong rubber. For the double-side stubbed plate, it can enhance the coupling of the flexural traveling wave and the local resonance modes, which can greatly enlarge the bandwidths. The new working mechanism and the related calculation results of the designed structures would provide an effective way for elastic metamaterial plate to broaden the FVBGs at low frequencies, which has potential applications in low-frequency vibration and noise attenuation.