Nonlinear dynamic analysis of the vibration energy harvester with hysteresis characteristics under random excitations

To optimize the design and operation of the piezoelectric energy harvesters (PEHs) in real-world applications, this research delves into the stochastic dynamics of vibration energy harvesters (VEHs) with hysteresis characteristics under random excitations. Initially, a set of models for integrable Duhem hysteresis VEHs are established to depict the electromechanical behavior of PEHs with hysteresis, determining both the potential and dissipated energy of the Duhem hysteretic component. Afterwards, the Duhem hysteretic VEHs under random excitations are equivalently replaced by a non-hysteretic nonlinear system. The stochastic averaging method is employed to derive the stationary distribution of mechanical states, subsequently enabling the theoretical determination of the mean square electric voltage (MSEV) and mean output power (MOP) of the VEHs. Finally, a sensitivity analysis is conducted to explore the impact of various parameters, including hysteresis parameters, excitation characteristics, and structural properties, on the harvester's output, aiming to guide design optimization. This study introduces a novel framework combining an integrable Duhem hysteresis model with stochastic averaging to analyze PEHs under random excitations, uniquely capturing soft-hardening hysteresis behaviors. And contributes a scientifically robust framework combining the Duhem hysteresis model with stochastic averaging, enabling precise analysis of PEHs under random excitations.