Vibration transmissibility of piezoelectric quasi-zero stiffness metastructures with linear and nonlinear shunts

Abstract This study investigates the dynamics of a piezoelectric quasi-zero stiffness metastructure controlled by linear and nonlinear shunts. An equivalent lumped-mass model of the metastructure with shunts is developed. The absolute displacement transmissibility of the metastructure is calculated analytically and numerically, with results from both methods showing strong agreement. Optimized shunt parameters are determined based on the linear transfer function of the system under base excitation, and the effects of linear and nonlinear shunts on the transmissibility are thoroughly analyzed. At a relatively high excitation level, the interaction between the resonant shunts and the metastructure splits the transmissibility curve into two branches, significantly reducing the peaks of the primary branch. When the excitation amplitude exceeds a threshold, severe detuning occurs, causing the separated branches to merge, which diminishes the control effectiveness of the shunts. Nonlinear shunts exhibit a higher critical detuning excitation amplitude compared to linear ones, as their resonance frequencies expand with increasing excitation amplitude. The metastructure’s resonance frequency increases at a faster rate than that of the nonlinear shunt, eventually causing the shunt to detune. By appropriately reducing the inductance to raise the shunt’s resonance frequency, the branches of the transmissibility curve can be effectively separated again, thereby reducing the amplitudes of the main branch.