Reliability and control of strongly nonlinear vibro-impact system under external and parametric Gaussian noises
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liability and control of strongly nonlinear vibro-impact system under external and parametric Gaussian noises 1,2
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LIU Li , XU Wei , YANG GuiDong & HUANG DongMei 1
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Department of Applied Mathematics, Northwestern Polytechnic University, Xi’an 710072, China; 2 School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China; 3 School of Mathematics and Statistics, Xidian University, Xi’an 710071, China Received January 13, 2020; accepted May 8, 2020; published online July 1, 2020
This paper mainly focuses on reliability and the optimal bounded control for maximizing system reliability of a strongly nonlinear vibro-impact system. Firstly, the new stochastic averaging in which the impact condition is converted to the system energy is applied to obtain the averaged Itô stochastic differential equation, by which the associated Backward Kolmogorov (BK) equation and Generalized Pontryagin (GP) equation are derived. Then, the dynamical programming equations are obtained based on the dynamical programming principle, by which the optimal bounded control for maximizing system reliability is devised. Finally, the effects of the bounded control and noise intensity on the reliability of the vibro-impact system are discussed in detail; meanwhile, the influence of impact conditions on the system’s reliability is also studied. The feasibility and effectiveness of the proposed analytical method are substantiated by numerical results obtained from Monte-Carlo simulation. vibro-impact system, first-passage failure, stochastic averaging method, stochastic optimal control Citation:
Liu L, Xu W, Yang G D, et al. Reliability and control of strongly nonlinear vibro-impact system under external and parametric Gaussian noises. Sci China Tech Sci, 2020, 63, https://doi.org/10.1007/s11431-020-1626-5
1 Introduction In recent years, vibro-impact systems have been a research hot spot, because it is extensively applied in mechanical and structural engineering such as the collision of the mechanical parts, structures interaction in piping systems [1] and nonlinear soil-structure interaction [2], heat exchanger tubes under aerodynamic excitation, and ship’s motion when colliding against fenders [3]. The existence of the impact could induce the appearance of rich and complicated phenomenon, especially the instability and unsafety of the system, thus, considering the relative problem of the vibro-impact systems has been an unavoidable issue. In order to utilize positive effect and eliminate the adverse effect of the non-smooth factors, a large number of in*Corresponding author (email: [email protected])
vestigations focused on the dynamical analysis of vibroimpact systems. Shaw and Holmes [4] researched the grazing bifurcation of vibro-impact systems. Luo [5] applied numerical simulation method to research the Torus bifurcation and Hopf bifurcation. Wagg [6] studied multi-sliding bifurcation phenomenon of a two degree-of-freedom vibroimpact system. Dimentberg and Iourtchenko [7–9] studied the stationary probability density
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