Theoretical modeling and analysis of a 2-degree-of-freedom hybrid piezoelectric–electromagnetic vibration energy harvester with a driven beam

In the article, a novel 2-degree-of-freedom hybrid piecewise-linear piezoelectric–electromagnetic vibration energy harvester is presented to achieve better energy harvesting efficiency. The harvester consists of a primary piezoelectric energy harvesting device to which an electromagnetic mechanism is coupled to improve the integral energy output, and a driven beam is mounted to broaden the operating bandwidth by inducing nonlinearity. Considering the piezoelectric–electromagnetic coupling characteristics and the nonlinear factors, dynamic equations of the system are established. Expressions of the output power are deduced though averaging method. Characteristic parameters are analyzed theoretically, including the piezoelectric parameters, electromagnetic parameters, and the piecewise-linearity. Frequency sweep excitation test is conducted on the setup at an excitation acceleration of 0.3 g and results demonstrate that two resonant regions are obtained with the peak output power of 5.4 and 6.49 mW, respectively, and the operating bandwidth is increased by 8 Hz. Moreover, though adjusting the stiffness of the driven beam k ₃ and the gap between the primary beam and the driven beam d, the performance of the harvester can be further optimized.