Nonlinear Synthetic Impedance Circuits for Vibration Attenuation in Piezoelectric Structures

Abstract

Piezoelectricity has been employed in a variety of engineering applications pertaining to vibration control and noise reduction using passive and active methods. Specifically, in the domain of piezoelectric shunt damping, predominantly linear or switching analog circuits have been implemented over the past several decades, mostly with a focus on linear structures. Low-frequency applications of piezoelectric shunt damping have also triggered the research on implementing synthetic impedance circuits to eliminate the need for bulky analog circuit components (e.g., large inductors). Most of the existing efforts on synthetic impedance shunts have been limited to emulating linear circuits. In this research, we explore nonlinear synthetic impedance-based piezoelectric structures through experiments and modeling, by introducing nonlinearities in the circuit domain. In the first part, we introduce a Duffing oscillator by means of a cubic synthetic inductance. The synthetic Duffing circuit is used as a nonlinear shunt circuit for a mechanically linear piezoelectric cantilever, and it is shown that the cubic nonlinearity can be introduced and programmed by varying the respective gain in the synthetic impedance circuit to change the bandwidth and bifurcation points in the frequency response. A nonlinear electromechanical model is developed, and numerical simulations are performed via time-domain solutions as well as approximate analytical solution using the method of harmonic balance. The next step following the hardening and softening Duffing oscillator cases is the nonlinear energy sink (NES) implementation for wideband vibration attenuation without a preferential linear resonance in the shunt. We explore the performance of the NES for a linear cantilever as well as a cantilever with dominant piezoelectric softening nonlinearity. Experiments are guided by numerical simulations throughout the work, and the underlying nonlinear electromechanical models are validated for various excitation amplitudes and nonlinear coefficients. Other than time-domain simulations and the method of harmonic balance, an alternative simulation approach is also proposed to explore the nonlinear vibration frequency response by means of machine learning for enhanced computational efficiency.