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TECHNICAL BRIEFS

Vibration Analysis of Non-Classically Damped Linear Systems

[+] Author and Article Information
Z. S. Liu, D. T. Song, C. Huang

Institute for Fuel Cell Innovation, National Research Council of Canada, Vancouver, BC, V6T 1W5, Canada e-mail: simon.liu@nrc.ca

D. J. Wang

Department of Mechanics, Peking University 100871, Beijing, P.R. China

S. H. Chen

Department of Mechanics, Jilin University 130025, Changchun, P.R. China

J. Vib. Acoust 126(3), 456-458 (Jul 30, 2004) (3 pages) doi:10.1115/1.1760563 History: Received November 01, 2002; Revised December 01, 2003; Online July 30, 2004
Copyright © 2004 by ASME
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References

Caughey,  T. K., and O’Kelly,  M. E. J., 1965, “Classically Normal Modes in Damped Linear Dynamics Systems,” ASME J. Appl. Mech., 32, pp. 583–588.
Liu,  M., and Wilson,  J., 1992, “Criterion for Decoupling Dynamic Equations of Motion of Linear Gyroscopic Systems,” AIAA J., 30, pp. 2989–2991.
Nicholson,  D. W., and Lin,  B., 1996, “Stable Response of Non-Classically Damped Mechanical Systems-II,” Appl. Mech. Rev., 49(10), part 2, pp. S49–S54.
Liu,  Z. S., and Huang,  C., 2002, “Evaluation of the Parametric Instability of an Axially Translating Media Using a Variational Principle,” J. Sound Vib., 257(5), pp. 985–995.
Chung,  K. R., and Lee,  C. W., 1986, “Dynamic Reanalysis of Weakly Non-Proportional DampedSystems,” J. Sound Vib., 111(1), pp. 37–50.
Meirovitch,  L., and Rayland,  G., 1979, “Response of Slightly Damped Gyroscopic Systems,” J. Sound Vib., 67(1), pp. 1–19.
Natsiavas,  S., and Beck,  J. L., 1998, “Almost Classically Damped Continuous Linear Systems,” ASME J. Appl. Mech., 65, pp. 1022–1031.
Inman,  D. J., and Andry,  A. N., 1980, “Some Results on the Nature of Eigenvalues of Discrete Damped Linear Systems,” ASME J. Appl. Mech., 47, pp. 927–930.

Figures

Grahic Jump Location
A two-degree-of-freedom non-classically damped system
Grahic Jump Location
Response x1(t) (h=π/2): the present method versus the exact solution
Grahic Jump Location
Response x2(t) (h=π/2): the present method versus the exact solution

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