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TECHNICAL PAPERS

Effective System Properties and Special Density in Random Vibration With Parametric Excitation

[+] Author and Article Information
S. Krenk, F. Rüdinger

Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark

Y. K. Lin

Center for Applied Stochastics Research, Florida Atlantic University, Boca Raton, FL 33431

J. Appl. Mech 69(2), 161-170 (Aug 13, 2001) (10 pages) doi:10.1115/1.1430665 History: Received January 22, 2001; Revised August 13, 2001
Copyright © 2002 by ASME
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References

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Lin,  Y. K., and Cai,  G. Q., 1988, “Exact Stationary-Response Solution for Second-Order Nonlinear Systems Under Parametric and External White-Noise Excitations: Part II,” ASME J. Appl. Mech., 55, pp. 702–705.
Cai,  G. Q., and Lin,  Y. K., 1988, “A New Approximate Solution Technique for Randomly Excited Non-linear Oscillators,” Int. J. Non-Linear Mech., 23, pp. 409–420.
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Krenk, S., 1999, “Energy and Spectral Density in Non-linear Random Response,” Stochastic Structural Dynamics, B. F. Spencer and E. A. Johnson, eds., Balkema, Rotterdam, pp. 43–51.
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Rüdinger, F., and Krenk, S., 2001, “Stochastic Analysis of Self-Induced Vibrations,” submitted to Meccanica, for publication.

Figures

Grahic Jump Location
Probability density of nondimensional energy; (a) α̃=0.5, (b) α̃=5
Grahic Jump Location
Auto-spectral density of position; (a) α̃=0.5,α=0.01, (b) α̃=0.5,α=0.1, (c) α̃=5,α=0.01, (d) α̃=5,α=0.1
Grahic Jump Location
Conditional expectations: (a) potential force via E[*|x], (b) exponent ψ(λ) and damping via E[*|λ]
Grahic Jump Location
Probability density pλ̃(λ̃); (a) ζ=0.05,ω0S110S22=0.0064, (b) ζ=0.1,ω0S110S22=0.012
Grahic Jump Location
Auto-spectral density Sx(ω)ω0x2; (a) ζ=0.05,ω0S110S22=0.0064, (b) ζ=0.1,ω0S110S22=0.012
Grahic Jump Location
Auto-spectral density Sx(ω)ω0x2; (a) ζ=0.05,ω0S110S22=0.0064, (b) ζ=0.1,ω0S110S22=0.012
Grahic Jump Location
Probability density px,ẋ(x,ẋ) for (a) α̃=0, (b) α̃=0.5, (c) α̃=5

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