Passive vibration control of subsonic thin plate via nonlinear capacitance and negative capacitance coupled piezoelectric shunt damping

As part of the aircraft wing, the thin plate is always affected by external airflow and harmonic excitation to generate undesirable nonlinear vibration behaviors, which will produce fatigue and damage to the aircraft. Therefore, it is necessary to develop some schemes for vibration control of subsonic thin plates. This work proposes a nonlinear piezoelectric shunt damping for nonlinear vibration control of subsonic thin plates. The nonlinear motion equation of the electromechanical coupling system is established by the extended Hamilton principle. The subsonic aerodynamic model is introduced by linear potential flow theory. Three different piezoelectric control circuits made up of inductance, resistance, nonlinear capacitance, and negative capacitance are considered. The nonlinear dynamic equations are solved by the Matcont toolbox. The first four generalized coordinates before and after the piezoelectric vibration control of the system are discussed. It can be observed that piezoelectric control has significant vibration suppression effects. The vibration control effects of three different piezoelectric control circuits are compared under different external excitation amplitude and airflow velocities. This study provides a relatively perfect piezoelectric control scheme for the vibration control of thin plates in subsonic airflow.