Power and electromechanical coupling of nonlinear piezoelectric vibration energy harvesters

In the past decade, nonlinearity has been introduced into piezoelectric energy harvesters (PEH) for power performance enhancement and bandwidth enlargement. While a great emphasis has been placed on the structural design and the effect of electrical part on the nonlinear dynamics of the system, the maximum power and power limit, an important aspect for performance optimization of nonlinear PEHs, are rarely studied, especially their relationship with that of linear PEHs. To this end, this paper is motivated to investigate the maximum power and power limit of a representative type of nonlinear PEHs, i.e., monostable. An equivalent circuit is proposed to analytically study and explain the behaviors of monostable PEHs, and reveals the connection between linear and monostable PEHs. The effect of nonlinearity, e.g., due to the additional magnetic force, is modeled as a nonlinear stiffness element mechanically and a nonlinear capacitive element electrically, based on the harmonic balance method. Facilitated by this equivalent circuit and the impedance matching technique, clear closed-form solutions of power limit and critical electromechanical coupling, i.e., minimum coupling to reach the power limit, of monostable PEHs are obtained. Then the effect of excitation level and magnetic field on the power and electromechanical coupling of the system is investigated. Though this paper uses monostable PEHs as an example, the results and technique can be extended to other similar types of nonlinear PEH systems as well, for example, bistable.