| Affiliation: | (1) State Key Laboratory of Vibration, Shock, and Noise, School of Mechanical and Power Energy Engineering, Shanghai Jiaotong University, Shanghai, 200030, China;(2) Department of Engineering Mechanics, Northwestern Polytechnical University, Xian, 710072, China;(3) Aircraft Strength Research Institute of China, Xian, 710065, China;(4) Institute of UAV, Northwestern Polytechnical University, Xian, 710072 |
| Abstract: | The Chebyshev polynomial approximation is applied to the dynamic response problem of a stochastic Duffing system with bounded random parameters, subject to harmonic excitations. The stochastic Duffing system is first reduced into an equivalent deterministic non-linear one for substitution. Then basic non-linear phenomena, such as stochastic saddle-node bifurcation, stochastic symmetry-breaking bifurcation, stochastic period-doubling bifurcation, coexistence of different kinds of steady-state stochastic responses, and stochastic chaos, are studied by numerical simulations. The main feature of stochastic chaos is explored. The suggested method provides a new approach to stochastic dynamic response problems of some dissipative stochastic systems with polynomial non-linearity. |
