Dongmei Huang¹, Dang Hong², Wei Li^1,*, Guidong Yang¹, Vesna Rajic³

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 509-524, 2024, DOI:10.32604/cmes.2023.029215 - 22 September 2023

Abstract In this paper, the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are investigated. Firstly, by means of the orthogonal polynomial approximation (OPA) method, the nonlinear damping and stiffness are expanded into the linear combination of the state variable. The condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of the mean value. Afterwards, the stochastic vibro-impact system can be turned into an equivalent high-dimensional deterministic non-smooth system. Two different Poincaré sections are chosen to analyze the bifurcation properties and… More >

Ying Zhang¹, Lin Du¹, Xiaole Yue¹, Qun Han¹, Tong Fang²

CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.1, pp. 37-51, 2015, DOI:10.3970/cmes.2015.106.037

Abstract The symmetry breaking bifurcation (SBB) phenomenon in a deterministic parameter Duffing system (DP-DS) is well known, yet the problem how would SBB phenomenon happen in a Duffing system with random parameter (RP-DS) is still open. For comparison study, the results for DP-DS are summarized at first: in short, SBB in DP-DS is just a transition of response phase trajectories from a single self-symmetric one about the origin into two mutual symmetric once, or vice versa. However, in DP-DS case, the two mutual symmetric phase trajectories are never commutable. In view of every sample of RP-DS… More >