The nonlinear dynamics analysis of stochastic delay Jeffcott rotor-seal system with the elastic support. (English) Zbl 1535.74365
Summary: The establishment of stochastic delay Jeffcott rotor-seal system not only considers the track irregularity caused by random noise and the possible influence of stochastic parameter excitation, but also considers the time-delay characteristics of sealing force. The rotation of the rotor shaft causes the gas in the chamber to produce a dynamic effect, resulting in a rotating force, which delays the feedback on the rotating shaft. Firstly, the one-dimensional average Itô differential equation is obtained by simplifying the infinite dimensional stochastic delay differential equation with the perturbation method. Secondly, the global and local stability of the rotor system are obtained by analyzing the singular boundary theory and the maximum Lyapunov exponent. Then, the conditions and types of stochastic bifurcation of rotor system are obtained by analyzing the steady-state joint probability density function. Finally, numerical simulation verifies the accuracy of the theoretical analysis, showing that the time delay affects rotor system to reach the stable critical speed for the first time, and the noise disturbance has a certain stability effect on the rotor system.
MSC:
| 74H50 | Random vibrations in dynamical problems in solid mechanics |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 74S60 | Stochastic and other probabilistic methods applied to problems in solid mechanics |
| 70K40 | Forced motions for nonlinear problems in mechanics |
| 70L05 | Random vibrations in mechanics of particles and systems |
Keywords:
rotor dynamics; average Itô differential equation; perturbation method; functional equation; noise disturbance; maximum Lyapunov exponent; stochastic bifurcationReferences:
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