An Improved Stochastic Averaging on the Piezoelectric Vibrational Harvester Model with Stiffness and Inertia Nonlinearities

• Published in: International journal of structural stability and dynamics Vol. 24; no. 8
• Main Authors: Li, Yusen, Ge, Gen
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 30.04.2024; World Scientific Publishing Co. Pte., Ltd
• Subjects: Damping; Differential equations; Electric potential; Energy harvesting; Inertia; Nonlinearity; Piezoelectricity; Probability density functions; Research Article; Stiffness coefficients; Voltage; stiffness nonlinearity; Gaussian white noise; Piezoelectric energy harvester; Gaussian colored noise; inertia nonlinearity
• ISSN: 0219-4554; 1793-6764
• DOI: 10.1142/S0219455424500846

In this paper, an improved stochastic averaging method is introduced to solve a monostable piezoelectric vibration energy harvester (VEH) model subject to basal Gaussian white and colored noises. First, the electric voltage is expressed as perturbations to the linear stiffness term and the damping term of the vibrational equation. Second, the original model is simplified into an Itô differential equation by the improved stochastic averaging method. Third, stationary solution of the Fokker–Plank–Kolmogorov function driven from the Itô equation is obtained, so that the stationary probability density functions (PDFs) of the displacement, velocity, and electrical voltage are obtained. With the help of the Monte Carlo, the effectiveness of these theoretical predictions is verified. Finally, the impacts of the nonlinear stiffness coefficient and nonlinear inertia coefficient on the responses are compared. It is found that the stiffness nonlinearity has stronger effect on the outputn electric voltage than the inertia nonlinearity.