The exit problem and global stability of a nonlinear oscillator excited by an ergodic real noise and harmonic excitations are examined. The real noise is assumed to be a scalar stochastic function of an n-dimensional Ornstein–Uhlenbeck vector process which is the output of a linear filter system. Due to the existence of t-dependent excitation, two two-dimensional Fokker–Planck–Kolmogorov (FPK) equations governing the van der Pol variables process and the amplitude-phase process, respectively, are obtained and discussed through a perturbation method and the spectrum representations of the FPK operator and its adjoint operator of the linear filter system, while the detailed balance condition and the strong mixing condition are removed. Based on these FPK equations, the global properties of one-dimensional nonlinear oscillators with external or (and) internal periodic excitations under external or (and) internal real noises can be examined. Finally, a Duffing oscillator excited by a parametric real noise and parametric harmonic excitations is presented as an example, and the mean first-passage time (MFPT) about the oscillator's exit behavior between limit cycles is obtained under both wide-band noise and narrow-band noise excitations. The analytical result is verified by digital simulation.
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On the Stochastic Dynamical Behaviors of a Nonlinear Oscillator Under Combined Real Noise and Harmonic Excitations
Chen Kong,
Chen Kong
State Key Laboratory of Mechanics and Control
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
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Zhen Chen,
Zhen Chen
State Key Laboratory of Mechanics and Control
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: czkillua@icloud.com
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: czkillua@icloud.com
Search for other works by this author on:
Xian-Bin Liu
Xian-Bin Liu
Professor
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
Search for other works by this author on:
Chen Kong
State Key Laboratory of Mechanics and Control
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: kongchen_bill@126.com
Zhen Chen
State Key Laboratory of Mechanics and Control
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: czkillua@icloud.com
of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: czkillua@icloud.com
Xian-Bin Liu
Professor
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
State Key Laboratory of Mechanics
and Control of Mechanical Structures,
Nanjing University of Aeronautics and
Astronautics,
Nanjing 210016, China
e-mail: xbliu@nuaa.edu.cn
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 27, 2016; final manuscript received September 3, 2016; published online December 5, 2016. Assoc. Editor: Stefano Lenci.
J. Comput. Nonlinear Dynam. May 2017, 12(3): 031015 (9 pages)
Published Online: December 5, 2016
Article history
Received:
June 27, 2016
Revised:
September 3, 2016
Citation
Kong, C., Chen, Z., and Liu, X. (December 5, 2016). "On the Stochastic Dynamical Behaviors of a Nonlinear Oscillator Under Combined Real Noise and Harmonic Excitations." ASME. J. Comput. Nonlinear Dynam. May 2017; 12(3): 031015. https://doi.org/10.1115/1.4034735
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