The dynamic stability of a two degrees-of-freedom system under bounded noise excitation with a narrowband characteristic is studied through the determination of moment Lyapunov exponents. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. For weak noise excitations, a singular perturbation method is employed to obtain second-order expansions of the moment Lyapunov exponents and Lyapunov exponents, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The different cases when the system is in subharmonic resonance, combination additive resonance, and combined resonance in the absence of noise, respectively, are considered. The effects of noise and frequency detuning on the parametric resonance are investigated.
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July 2009
Research Papers
Parametric Resonance of a Two Degrees-of-Freedom System Induced by Bounded Noise
Jinyu Zhu,
Jinyu Zhu
Department of Civil and Environmental Engineering, Faculty of Engineering,
e-mail: j7zhu@engmail.uwaterloo.ca
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
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W.-C. Xie,
W.-C. Xie
Department of Civil and Environmental Engineering, Faculty of Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
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Ronald M. C. So,
Ronald M. C. So
Department of Mechanical Engineering,
The Hong Kong Polytechnic University
, Hung Hom, Kowloon, Hong Kong
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X. Q. Wang
X. Q. Wang
Department of Mechanical Engineering,
The Hong Kong Polytechnic University
, Hung Hom, Kowloon, Hong Kong
Search for other works by this author on:
Jinyu Zhu
Department of Civil and Environmental Engineering, Faculty of Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canadae-mail: j7zhu@engmail.uwaterloo.ca
W.-C. Xie
Department of Civil and Environmental Engineering, Faculty of Engineering,
University of Waterloo
, Waterloo, ON, N2L 3G1, Canada
Ronald M. C. So
Department of Mechanical Engineering,
The Hong Kong Polytechnic University
, Hung Hom, Kowloon, Hong Kong
X. Q. Wang
Department of Mechanical Engineering,
The Hong Kong Polytechnic University
, Hung Hom, Kowloon, Hong KongJ. Appl. Mech. Jul 2009, 76(4): 041007 (13 pages)
Published Online: April 22, 2009
Article history
Received:
January 25, 2008
Revised:
September 16, 2008
Published:
April 22, 2009
Citation
Zhu, J., Xie, W., So, R. M. C., and Wang, X. Q. (April 22, 2009). "Parametric Resonance of a Two Degrees-of-Freedom System Induced by Bounded Noise." ASME. J. Appl. Mech. July 2009; 76(4): 041007. https://doi.org/10.1115/1.2999427
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