Stochastic averaging of energy harvesting systems

• Published in: International journal of non-linear mechanics Vol. 85; pp. 174 - 187
• Main Authors: Jiang, Wen-An, Chen, Li-Qun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2016
• Subjects: Computer simulation; Density; Displacement; Energy harvesting; Gaussian white noise; Mathematical analysis; Monte Carlo simulation; Nonlinearity; Parametric excitation; Partial differential equations; Stochastic averaging method; Stochasticity; Gaussian white noise; Parametric excitation; Stochastic averaging method; Energy harvesting; Monte Carlo simulation
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2016.07.002

A stochastic averaging method is proposed for nonlinear energy harvesters subjected to external white Gaussian noise and parametric excitations. The Fokker–Planck–Kolmogorov equation of the coupled electromechanical system of energy harvesting is a three variables nonlinear parabolic partial differential equation whose exact stationary solutions are generally hard to find. In order to overcome difficulties in solving higher dimensional nonlinear partial differential equations, a transformation scheme is applied to decouple the electromechanical equations. The averaged Itô equations are derived via the standard stochastic averaging method, then the FPK equations of the decoupled system are obtained. The exact stationary solution of the averaged FPK equation is used to determine the probability densities of the displacement, the velocity, the amplitude, the joint probability densities of the displacement and velocity, and the power of the stationary response. The effects of the system parameters on the output power are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the Monte Carlo simulations. •A stochastic averaging method is proposed for nonlinear energy harvesting systems.•A transformation is used to decouple the electromechanical equations.•The analytical outcomes are supported by the Monte Carlo simulations.