Metamaterial beam with graded local resonators for broadband vibration suppression

Abstract

This paper investigates a technique for broadband vibration suppression using a graded metamaterial beam. A series of local resonators with the same mass but different natural frequencies are attached to the beam. The difference between the natural frequencies of neighboring local resonators is defined as the frequency spacing. The spectral element method (SEM) is used to model the graded metamaterial beam, and is verified by the corresponding finite element model (FEM). Three figures of merit are defined to quantitatively evaluate the vibration suppression performance of the proposed metamaterial beam, in terms of the attenuation bandwidth and attenuation strength. Subsequently, a design strategy is proposed, and used to tune the frequency spacing to get a wide attenuation region. A parametric study is conducted to reveal the effects of the frequency spacing and damping ratio on the vibration suppression performance of the graded metamaterial beam: with increasing frequency spacing, the attenuation region first becomes wider, then multiple discrete attenuation regions appear; and with increasing damping ratio, the transmittance response becomes flatter. A piezoelectric metamaterial beam is used to implement the proposed design strategy. Using a synthetic shunt circuit, the ‘stiffness’ of the local resonator can be tuned using a piezoelectric transducer. The FEM simulation results agree well with the developed theory for the graded metamaterial beam: with tuning of the capacitance spacing (2.4 nF), the attenuation bandwidth can be increased by about 172.8% as compared to the conventional one shunted with identical capacitances.