Tunable nonlinear piezoelectric metabeams for multimode vibration suppression

Vibration suppression, especially over a wide band at low frequencies, is a long-standing and challenging problem. Here, the design method and mechanism of using nonlinear synthetic impedance circuits to suppress vibrations of piezoelectric metabeams is explored. We first investigate the dynamic characteristics of a nonlinear piezoelectric unit cell under different nonlinear coefficients with a reduced-order finite element model. Numerical results show that the nonlinear coefficients required to suppress vibration differ by an order of magnitude for distinct resonant peaks. Besides, it is discovered that while some nonlinear coefficients can attenuate resonant peaks by transferring the mechanical energy to the circuit and dissipating, 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 can be tuned to suppress vibration in a wide band within 400 Hz, showing notable robustness to different resistance and excitation levels. A piezoelectric metabeam experiment was conducted to verify the findings. The consistency of simulated and measured transmissibility validates the feasibility of tunable multimode vibration suppression by harnessing circuit nonlinearity.