The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real...The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.展开更多
The generalized cell mapping(GCM) method is used to obtain the stationary response of a single-degree-of-freedom.Vibro-impact system under a colored noise excitation. In order to show the advantage of the GCM method, ...The generalized cell mapping(GCM) method is used to obtain the stationary response of a single-degree-of-freedom.Vibro-impact system under a colored noise excitation. In order to show the advantage of the GCM method, the stochastic averaging method is also presented. Both of the two methods are tested through concrete examples and verified by the direct numerical simulation. It is shown that the GCM method can well predict the stationary response of this noise-perturbed system no matter whether the noise is wide-band or narrow-band, while the stochastic averaging method is valid only for the wide-band noise.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11172233,11302169,11302170,and 11472212)the Fundamental Research Funds for the Central Universities(No.3102014JCQ01079)
文摘The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.
基金supported by the National Natural Science Foundation of China (Grant No. 11772149)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,China (Grant No. MCMS-I-19G01)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD),China。
文摘The generalized cell mapping(GCM) method is used to obtain the stationary response of a single-degree-of-freedom.Vibro-impact system under a colored noise excitation. In order to show the advantage of the GCM method, the stochastic averaging method is also presented. Both of the two methods are tested through concrete examples and verified by the direct numerical simulation. It is shown that the GCM method can well predict the stationary response of this noise-perturbed system no matter whether the noise is wide-band or narrow-band, while the stochastic averaging method is valid only for the wide-band noise.
