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TECHNICAL PAPERS

First-Passage Failure of Quasi-Integrable Hamiltonian Systems

[+] Author and Article Information
W. Q. Zhu, M. L. Deng, Z. L. Huang

Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. Chinaand State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Science, Beijing 100008, P. R. China

J. Appl. Mech 69(3), 274-282 (May 03, 2002) (9 pages) doi:10.1115/1.1460912 History: Received February 28, 2001; Revised September 27, 2001; Online May 03, 2002
Copyright © 2002 by ASME
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Figures

Grahic Jump Location
Reliability function of system (24) for given initial condition. α11=0.01,α12=0.03,β1=0.1,ω1=1.0,α21=0.04,α22=0.04,β2=0.4,ω2=0.707,2D1=0.03,2D2=0.01,Hc=0.3. The other parameters are 2D3=2D4=0,H10=H20=0 for A and A ′ ; 2D3=2D4=0,H10=0.09,H20=0.03 for B and B ′ ; 2D3=0.1,2D4=0.01,H10=H20=0 for C and C ′ . –analytical result by using the present proposed procedure; – – – –analytical result by using the procedure proposed in 24; ○ ⋄ ▵ from digital simulation.
Grahic Jump Location
Probability density of first-passage time of system (24) for given initial condition. The parameters and symbols are the same as those in Fig. 2.
Grahic Jump Location
Mean first-passage time of system (24) as function of H10 for given H20.2D3=2D4=0,H20=0 for A and A ′ ; 2D3=2D4=0,H20=0.08 for B and B ′ ; 2D3=0.1,2D4=0.01,H20=0 for C and C ′ . The other parameters and symbols are the same as those in Fig. 2.
Grahic Jump Location
Reliability of system (24) at t=2 (second) as function of H10 and H20.2D3=0.1,2D4=0.01. The other parameters are the same as those in Fig. 2.
Grahic Jump Location
Probability density of first-passage time of system (24) as function of H20 and t for given H10=0.2D3=0.1,2D4=0.01. The other parameters are the same as those in Fig. 2.
Grahic Jump Location
Mean first-passage time of system (24) as function of H10 and H20.2D3=0.1,2D4=0.01. The other parameters are the same as those in Fig. 2.
Grahic Jump Location
Reliability function of system (52) for given initial condition. α1=0.2,α2=0.1,α3=0.1,β1=0.05, ω=1.0; α4=0.4,β2=0.1,k=2.0,2D1=0.03,2D2=0.01,Hc=0.3. The other parameters are 2D3=2D4=0,H10=H20=0 for A and A ′ ; 2D3=2D4=0,H10=0.04,H20=0.02 for B and B ′ ; 2D3=0.1,2D4=0.05,H10=H20=0 for C and C ′ . –analytical result by using the present proposed procedure; – – – –analytical result by using the procedure proposed in 24; ○ ⋄ ▵ from digital simulation.
Grahic Jump Location
Probability density of first-passage time of system (52) for given initial condition. The parameters and symbols are the same as those in Fig. 8.
Grahic Jump Location
Mean first-passage time of system (52) as function of H20 for given H10.2D3=2D4=0,H10=0 for A and A ′ ; 2D3=2D4=0,H10=0.04 for B and B ′ ; 2D3=0.1,2D4=0.05,H10=0 for C and C ′ . The other parameters and symbols are the same as those in Fig. 8.
Grahic Jump Location
Safety domain Ω and its boundary on plane H1 and H2 for system (24)

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