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TECHNICAL PAPERS

Moment Lyapunov Exponents of a Two-Dimensional Viscoelastic System Under Bounded Noise Excitation

[+] Author and Article Information
W.-C. Xie

Solid Mechanics Division, Faculty of Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada

J. Appl. Mech 69(3), 346-357 (May 03, 2002) (12 pages) doi:10.1115/1.1445143 History: Received April 24, 2001; Revised October 02, 2001; Online May 03, 2002
Copyright © 2002 by ASME
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References

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Ariaratnam, S. T., 1996, “Stochastic Stability of Viscoelastic Systems Under Bounded Noise Excitation,” IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics, A. Naess and S. Krenk, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 11–18.
Arnold, L., Oeljeklaus, E., and Pardoux, E., 1986, “Almost Sure and Moment Stability for Linear Ito⁁ Equations,” Lyapunov Exponents (Lecture Notes in Mathematics, 1186), L. Arnold and V. Wihstutz, eds., Springer-Verlag, Berlin, pp. 85–125.
Arnold, L., Kliemann, W., and Oeljeklaus, E., 1986, “Lyapunov Exponents of Linear Stochastic Systems,” Lyapunov Exponents (Lecture Notes in Mathematics, 1186), L. Arnold and V. Wihstutz, eds., Springer-Verlag, Berlin, pp. 129–159.
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Xie,  W.-C., 2001, “Moment Lyapunov Exponents of a Two-Dimensional System Under Real Noise Excitation,” J. Sound Vib., 239, No. 1, pp. 139–155.
Xie, W.-C., 2000, “Moment Lyapunov Exponents of a Two-Dimensional System under Bounded Noise Parametric Excitation,” J. Sound Vib., submitted for publication.
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Figures

Grahic Jump Location
Moment Lyapunov exponent Λx(t)(p). ε=0.05, μ=1, κ=5, γ=0, σ=0.5.
Grahic Jump Location
Moment Lyapunov exponent Λx(t)(p). ε=0.05, μ=1, κ=5, γ=0, σ=1.
Grahic Jump Location
Moment Lyapunov exponent Λx(t)(p). ε=0.05, μ=1, κ=5, γ=1, σ=0.25.
Grahic Jump Location
Moment Lyapunov exponent Λx(t)(p). ε=0.05, μ=1, κ=5, γ=1, σ=0.5.
Grahic Jump Location
Moment Lyapunov exponent Λx(t)(p). ε=0.05, μ=1, κ=5, γ=1, σ=1.
Grahic Jump Location
Moment Lyapunov exponent Λq(τ)(p). ε=0.05, c0=1,p0=0,ω0=1,μ0=1,κ0=5,γ0=0,σ0=0.5.
Grahic Jump Location
Moment Lyapunov exponent Λq(τ)(p). ε=0.05, c0=1,p0=0,ω0=1,μ0=1,κ0=5,γ0=1,σ0=0.5.
Grahic Jump Location
Lyapunov exponent λq(τ). ε=0.05, c0=0,p0=0,ω0=1,κ0=5,γ0=0,σ0=0.5.
Grahic Jump Location
Lyapunov exponent λq(τ). ε=0.05, c0=0,p0=0,ω0=1,κ0=5,γ0=0.5,σ0=0.5.
Grahic Jump Location
Lyapunov exponent λq(τ). ε=0.05, c0=0,p0=0,ω0=1,κ0=5,γ0=1,σ0=0.5.

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