Melnikov-method-based broadband mechanism and necessary conditions of nonlinear rotating energy harvesting using piezoelectric beam

Nonlinearity can be used to enhance broadband rotating piezoelectric vibration energy harvesting, but how to construct a proper nonlinear rotating harvester is a challenging problem in engineering applications. This article presents a Melnikov-theory-based method to explore broadband mechanism and necessary conditions of nonlinear rotating piezoelectric vibration energy harvesting system. First, a perturbed state-space representation of nonlinear rotating energy harvesting system is built based on its dynamic model. It can be seen that bi-stability of the unperturbed nonlinear system is the physical basis of achieving broadband and low-frequency rotating energy harvesting. Second, the Melnikov function is defined to derive two necessary conditions of homoclinic bifurcation and chaotic motions. Then simulations are performed to identify the key parameters and their effects on the Melnikov conditions, including distance, rotating frequency, and excitations. It can be seen that homoclinic bifurcation and chaotic motions can occur in nonlinear rotating energy harvesting systems under single-frequency and broadband excitations. Finally, the experiments are carried out to validate the two necessary conditions. The results demonstrate that the proposed method can provide important guidelines for optimally designing nonlinear rotating piezoelectric energy harvesters in practice.