Abstract
The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Ito stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
