Optimal dual-functional design for a piezoelectric autoparametric vibration absorber

•The nonlinear saturation principle and 1:2 internal resonance are used for AVA.•The theoretical model is verified by the experimental data of a novel prototype.•Approximate analytical solutions are obtained using the method of multiple scales.•The unstable region is adjustable by the electrical damping for improved vibration control.•The optimized system is able to perform well in the environment with small external noises. The nonlinear saturation principle and 1:2 internal resonance are used in the design of the piezoelectric autoparametric vibration absorber for vibration suppression and energy harvesting. A novel prototype is manufactured. The proposed theoretical model is verified by the experimental data. Synergy optimization is performed based on the approximate analytical solutions obtained using the harmonic balance method and the method of multiple scales. By leveraging the Routh-Hurwitz criterion, the system’s stability boundary is analytically determined and confirmed by the numerical simulation of the original full coupled governing equations. The system undergoes periodic motion, aperiodic motion and chaos successively from the stable region to the center of the unstable region. The unstable region is shown to be adjustable and minimized by the maximal electrical damping to improve the vibration suppression. The design proposed for the minimal base (main structure) displacement at resonance locates in the stable zone. The optimized piezoelectric autoparametric absorber not only effectively mitigates the vibration of the main structure but also harvests large electric power at resonance or near resonance. Such a system is shown to perform well in the environment with small external noises.