高斯色噪声激励下的高速转子轴承系统的P-分岔分析
P-Bifurcation Analysis of High-Speed Rotor-Bearing System under Excited byGaussian Color Noise
DOI: 10.12677/aam.2025.149409, PDF,    科研立项经费支持
作者: 邓生文*：广东理工学院基础课教学研究部，广东 肇庆；叶正伟：广东科技学院通识教育学院，广东 东莞
关键词: 高速转子轴承系统；高斯色噪声；随机平均法；P-分岔；High-Speed Rotor-Bearing System； Gaussian Color Noise； Stochastic Average Method； P-Bifurcation
摘要: 对高速转子轴承系统引入高斯色噪声，根据统一色噪声近似原理将色噪声白化，得到白噪声激励的等效非线性模型，运用拟不可积Hamilton理论随机平均法得到Itô微分方程，并求出FPK方程和对应的概率密度函数。最后根据概率密度函数分析随机P-分岔，并进行数值模拟验证。
Abstract: The Gaussian color noise is introduced into the High-Speed Rotor-Bearing system, and the equivalent nonlinear model of white noise excitation is obtained according to the uniform colored noise approximation theory. The Itô differential equation is obtained by the stochastic average method of quasi-non-integrable Hamilton theory, and the FPK equation and the corresponding probability density function are obtained. Finally, the stochastic P-bifurcation is analyzed according to the probability density function and verified by numerical simulation.
文章引用：邓生文, 叶正伟. 高斯色噪声激励下的高速转子轴承系统的P-分岔分析[J]. 应用数学进展, 2025, 14(9): 157-164. https://doi.org/10.12677/aam.2025.149409

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