Multimode Vibration Suppression of Piezoelectric Metabeams with Tunable Nonlinear Coefficients

Abstract

Vibration suppression, especially over a wide band at low frequencies, is a long-standing and challenging problem. Recently, nonlinear piezoelectric metabeams have shown potential in vibration control, owing to the flexibility in nonlinear circuit design. Here, a reduced-order finite element model is established and the nonlinear coefficients are readily available by employing a synthetic impedance shunt. We first investigate the dynamic characteristics of a nonlinear piezoelectric unit cell under different nonlinear coefficients. Numerical results show that the nonlinear coefficients required to suppress vibration differ by an order of magnitude for distinct resonant peaks. Besides, we discover that while some nonlinear coefficients can attenuate resonant peaks, they meanwhile amplify vibrations at slightly lower frequencies prior to the resonant peaks, both suppression and amplification are accompanied by quasiperiodic and chaotic behaviors. Therefore, we propose a piezoelectric unit cell with tunable cubic nonlinear coefficients dependent on the excitation frequency, avoiding vibration amplification. With this design method, it is demonstrated that the piezoelectric metabeam consisting of 15 unit cells can be tuned to suppress vibration in a wide band from 5 to 300 Hz, showing strong robustness to different resistance and excitation levels. This tunable nonlinear piezoelectric metabeam shows a promising prospect for low-frequency vibration suppression by harnessing circuit nonlinearity.

Keywords: nonlinear piezoelectric metamaterials, cubic nonlinearity, synthetic impedance circuits, vibration control