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Research Papers

Stability of SDOF Linear Viscoelastic System Under the Excitation of Wideband Noise

[+] Author and Article Information
Qinghua Huang, Wei-Chau Xie

Department of Civil and Environmental Engineering, University of Waterloo, ON, N2L 3G1, Canada

J. Appl. Mech 75(2), 021012 (Feb 25, 2008) (9 pages) doi:10.1115/1.2775496 History: Received June 09, 2006; Revised July 08, 2007; Published February 25, 2008

The moment Lyapunov exponents of a single degree-of-freedom viscoelastic system under the excitation of a wideband noise are studied in this paper. A realistic example of such a system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The method of averaging, both first order and second order, is applied. The averaged Itô differential equation governing the pth norm is established and the pth moment Lyapunov exponent is then obtained. White noise and real noise are considered as models of wideband noises. The variations of the moment Lyapunov exponents with the change of different parameters are discussed.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Moment Lyapunov exponents under white noise excitation for different ε and σ

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Figure 2

Moment Lyapunov exponents under white noise excitation

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Figure 3

Moment Lyapunov exponents under white noise excitation

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Figure 4

Moment Lyapunov exponents under real noise excitation for different γ

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Figure 5

Moment Lyapunov exponents under real noise excitation for different κ

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Figure 6

Moment Lyapunov exponents under real noise excitation for different α

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Figure 7

Moment Lyapunov exponents under real noise excitation

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Figure 8

Moment Lyapunov exponents under real noise excitation

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