Attaining Nonlinear Hardening Stiffness in Piezoelectric Vibration Applications Using Passive Nonlinear P-N Junction Capacitance

Piezoelectric vibration isolation and energy harvesting applications has been studied extensively. Nonlinear approaches may provide better performance over a broader frequency range. Nonlinearity can be introduced in the mechanical domain or electrical domain actively or passively. Since electrical components can be in smaller scales compared to mechanical counterparts, nonlinearity in the electrical domain can be more practical and convenient. Moreover, passive structures require no energy supply and controller therefore they are simpler and more reliable than active ones. In this paper, a novel way to attain passive hardening stiffness was presented for piezoelectric vibration isolation or energy harvesting. Nonlinearity was suggested to be attained with use of nonlinear capacitance of P-N junction in electrical domain and its capacitance model is introduced. A piezoelectric patch operating in d33 mode is considered and modelled as a single degree of freedom (SDOF) linear stiffness element without internal damping. force vs. displacement curves obtained by the models and finite element method (FEM) showed that hardening stiffness can be achieved. Frequency domain analysis is conducted for hardening stiffness and effect of piezoelectric coupling coefficient on resonance frequencies investigated. It is explored that resonances of nonlinear frequency response curves are bounded by open and short circuit resonance frequencies. Lastly, whether theoretically analyzed hardening capacitor is realizable or not is discussed.