o:35829 Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method en 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 the impact numbers are identified for the periodic response. Consequently, the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear system. Furthermore, the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic system. It can be found that the excitation frequency can induce period-doubling bifurcation and grazing bifurcation. Increasing the random intensity may result in a diffusion-based trajectory and the impact with the constraint plane, which induces the topological behavior of the non-smooth system to change drastically. It is also found that grazing bifurcation appears in advance with increasing of the random intensity. The stronger impulse force can result in the appearance of the diffusion phenomenon. KEYWORDS: Orthogonal polynomial approximation; vibro-impact systems; non-smooth systems; grazing bifurcation 1552101 1526-1492 1552099 10.32604/cmes.2023.029215 2025-02-05T12:51:13.257Z 44 no 46 Dongmei Huang Dang Hong person Wei Li person Guidong Yang person Vesna Rajić University of Belgrade Faculty of Economics person application/pdf 2063530 https://phaidrabg.bg.ac.rs/o:35829 no yes 16 70 1552253 11A03 CMES - Computer Modeling in Engineering and Sciences 138 1 509 524 2024