Energy harvesting of monostable Duffing oscillator under Gaussian white noise excitation

•The Fokker–Plank–Kolmogorov equation is derived from the governing equations.•The Van Kampen expansion is applied to determine the statistical moments.•The effects of related parameters on the output voltage are numerically demonstrated.

Energy harvesting of monostable Duffing oscillator with piezoelectric coupling under Gaussian white noise excitation is investigated. Based on the Fokker–Plank–Kolmogorov equation of piezoelectric coupling systems, the statistical moments of the response are derived from the Van Kampen expansion. The effects of the spectral density of the random excitation and the coefficient of cubic nonlinearity on the expected response moments are analyzed. Some numerical examples are presented to demonstrate the effects of excitation spectral density, coefficient of cubic nonlinearity and initial conditions on the output voltage.