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TECHNICAL PAPERS

Forced Vibration Analysis for Damped Periodic Systems With One Nonlinear Disorder

[+] Author and Article Information
H. C. Chan, Y. K. Cheung

Department of Civil and Structural Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

C. W. Cai

Department of Mechanics, Zhongshan University, Guangzhou 510275, P. R. China

J. Appl. Mech 67(1), 140-147 (Dec 28, 1998) (8 pages) doi:10.1115/1.321158 History: Received June 10, 1998; Revised December 28, 1998
Copyright © 2000 by ASME
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References

Li,  D., and Benaroya,  H., 1992, “Dynamics of Periodic and Near-Periodic Structures,” ASME Appl. Mech. Rev., 45, pp. 447–459.
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Vakakis, A. F., Manvetich, L. I., Mikhlin, Y. V., Pilipchuk, V. N. and Zevin, A. A., 1996, Normal Modes and Localization in Nonlinear Systems, Wiley, New York.
Liu,  J. K., Zhao,  L. C., and Fang,  T., 1995, “A Geometric Theory in Investigation on Mode Localization and Frequency Loci Veering Phenomena,” ACTA Mech. Solida Sinica, 8, pp. 349–355.
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Vakakis,  A. F., King,  M. E., and Pearlstein,  A. J., 1994, “Forced Localization in a Periodic Chain of Nonlinear Oscillators,” Int. J. Non-Linear Mech., 29, pp. 429–447.
Cai,  C. W., Cheung,  Y. K., and Chan,  H. C., 1988, “Dynamic Response of Infinite Continuous Beams Subjected to a Moving Force—An Exact Method,” J. Sound Vib., 123, pp. 461–472.
Cai,  C. W., Cheung,  Y. K., and Chan,  H. C., 1990, “Uncoupling of Dynamic Equations for Periodic Structures,” J. Sound Vib., 139, pp. 253–263.
Cai,  C. W., Cheung,  Y. K., and Chan,  H. C., 1995, “Mode Localization Phenomena in Nearly Periodic Systems,” ASME J. Appl. Mech., 62, pp. 141–149.
Cai,  C. W., Chan,  H. C., and Cheung,  Y. K., 1997, “Localized Modes in Periodic Systems With Nonlinear Disorders,” ASME J. Appl. Mech., 64, pp. 940–945.
Meirovitch, L., 1975, Elements of Vibration Analysis, McGraw-Hill, New York.
Skudrzyk, E. J., 1968, Simple and Complex Vibratory Systems, Pennsylvania State University Press, University Park, PA.
Skudzryk,  E. J., 1980, “The Mean Value Method of Predicting the Dynamic Response of Complex Vibrators,” J. Acoust. Soc. Am., 67, pp. 1105–1135.
Igusa,  T., and Tang,  Y., 1992, “Mobilities of Periodic Structures in Terms of Asympotic Modal Properties,” AIAA J., 30, pp. 2520–2525.

Figures

Grahic Jump Location
Damped periodic system with a nonlinear disorder; (a) original system with n number of subsystems, (b) equivalent system with cyclic periodicity and 2n number of subsystems
Grahic Jump Location
The frequency response (|As0|−Ω/ω0) curve

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