Statistical linearization for random vibration energy harvesting with piezoelectric material nonlinearity

Due to piezoelectric softening and dissipative nonlinearities, the piezoelectric cantilever energy harvester exhibits nonlinear hysteresis when subjected to large excitation. These nonlinearities have brought significant challenges to the modeling and response prediction of randomly excited piezoelectric energy harvesting systems. In this study, the voltage responses of the nonlinear piezoelectric cantilever energy harvester under random excitation are initially assumed to follow the Gaussian distribution which is experimentally validated later. The equivalent linear transfer function are derived from the approximate linearization of the stiffness and damping using the statistical linearization (SL) technique. The mathematical expectations of the voltage responses are calculated from the multivariate normal distributions. Frequency sweep experiments are conducted to a cantilever energy harvester to identify the nonlinear piezoelectric material properties. The statistically linearized model was experimentally validated under random base acceleration excitation by comparing the probability density function of the predicted voltage responses and average power against the experimental measurements. The advantage of the SL technique lies in allowing one to use an iterative procedure to estimate the equivalent linear terms while the analytical expressions are unattainable because of the complex nonlinearity in the governing equations. The results show that the prediction of the SL model to the random base acceleration excitation agrees with experimental measurements with a broadband frequency range, although only the fundamental mode of the beam is considered.