Theoretical Analysis of the Power Performance of a Monostable Galloping-Based Piezoelectric Energy Harvester

In the past few years, different kinds of structural nonlinearities, such as external magnetic interaction and multistable structures, have been introduced into galloping energy harvesters to enhance energy harvesting efficiency. However, since the galloping-based piezoelectric energy harvester (GPEH) is a self-excited system, the conventional impedance matching method that is widely used in vibration energy harvesters is no longer valid for it. Therefore, the power characteristics of the nonlinear GPEH are still an open question to be solved. To this end, this paper is motivated to derive the approximate analytical solution of a monostable galloping-based piezoelectric energy harvester through the harmonic balance method and impedance matching theory. The analytical maximum power, power limit, and critical electromechanical coupling are studied from the perspective of the influence of structural nonlinearity on the power performance. Firstly, the approximate analytical solutions of output power, power limit, optimal resistance, and critical electromechanical coupling coefficient are derived. The accuracy of the analytical solution is verified by numerical simulation. It is found that the influence of structural nonlinearity on the power characteristics of the nonlinear GPEH is quite different under different wind speeds. After that, the power characteristics of the system under different wind speeds and different coupling conditions are investigated. The results showed that the maximum power of the system can be increased by introducing stiffness nonlinearity under low wind speed and weakly coupled configuration. Even more, the system can be shifted into a strongly coupled system when the nonlinearity is enhanced to a certain level. Reasonable design of stiffness nonlinearity can effectively reduce the critical electromechanical coupling, which indicates that stiffness nonlinearity is a feasible and effective way to improve the power performance of low-speed wind energy harvesting.