0
Research Papers

Parametric Resonance of a Two Degrees-of-Freedom System Induced by Bounded Noise

[+] Author and Article Information
Jinyu Zhu

Department of Civil and Environmental Engineering, Faculty of Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadaj7zhu@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, X. Q. Wang

Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

J. Appl. Mech 76(4), 041007 (Apr 22, 2009) (13 pages) doi:10.1115/1.2999427 History: Received January 25, 2008; Revised September 16, 2008; Published April 22, 2009

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Lyapunov exponent for β1=β2=0 and ν0=2ω1

Grahic Jump Location
Figure 2

Moment Lyapunov exponent for β1=β2=0, and ν0=2ω1(K=12)

Grahic Jump Location
Figure 3

Lyapunov exponent for β1=β2=0, and ν0=ω1+ω2

Grahic Jump Location
Figure 4

Moment Lyapunov exponent for β1=β2=0 and ν0=ω1+ω2(K=20)

Grahic Jump Location
Figure 5

Moment Lyapunov exponent for β1=0.2, β2=0.1, and ν0=ω1+ω2

Grahic Jump Location
Figure 6

Moment Lyapunov exponent for β1=0.2, β2=0.1, and ν0=ω1+ω2

Grahic Jump Location
Figure 7

Lyapunov exponent for β1=0.2, β2=0.1, and ν0=ω1+ω2

Grahic Jump Location
Figure 8

Moment Lyapunov exponent for β1=β2=0.1, and ν0=ω1+ω2

Grahic Jump Location
Figure 9

Moment Lyapunov exponent for β1=0.2, β2=0.1, and ν0=ω1+ω2

Grahic Jump Location
Figure 10

Lyapunov exponent for β1=β2=0, ω1=ω2, and ν0=2ω1

Grahic Jump Location
Figure 11

Lyapunov exponent for β1=β2=0, ω1=ω2, and ν0=2ω1

Grahic Jump Location
Figure 12

Lyapunov exponent for β1=β2=0.2, ω1=ω2, and ν0=2ω1

Grahic Jump Location
Figure 13

Moment Lyapunov exponent for β1=β2=0, ω1=ω2, and ν0=2ω1(K=20)

Grahic Jump Location
Figure 14

Moment Lyapunov exponent for β1=β2=0.2, ω1=ω2, and ν0=2ω1

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In