Non-stationary response of variable-mass Duffing oscillator with mass disturbance modeled as Gaussian white noise

Jie Cui, Wen-An Jiang, Zhao-Wang Xia and Li-Qun Chen

Physica A: Statistical Mechanics and its Applications, 2019, vol. 526, issue C

Abstract: This paper investigates the probability density evolution process of a variable-mass Duffing oscillator with mass disturbance modeled as Gaussian white noise. For small mass disturbance, the transition probability density function (TPDF) solution of the variable-mass system is calculated by using path integration method. The corresponding Fokker–Planck–Kolmogorov (FPK) equation of the approximate mass disturbance system are derived. The solution procedure based on Gauss–Legendre quadrature integration rule is formulated to obtain and study the probabilistic solutions of the strongly and weekly nonlinear variable-mass system. Different values of excitation intensity are used to examine the effectiveness of the proposed method. Compared with the Monte Carlo simulation results, good agreement is achieved with the path integration method. For large mass disturbance, the probability density evolution process are numerically calculated via the fourth order Runge–Kutta algorithm.

Keywords: Variable-mass system; Path integration; Probability density function; Nonlinear (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119306284

DOI: 10.1016/j.physa.2019.04.254

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