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http://dx.doi.org/10.5050/KSNVE.2010.20.9.849

Nonlinear Oscillation Characteristics in Combination Resonance Region Considering Damping Effects  

Jeong, Tae-Gun (건국대학교 기계공학부)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.20, no.9, 2010 , pp. 849-855 More about this Journal
Abstract
Damping may change the response characteristics of nonlinear oscillations due to the parametric excitation of a thin cantilever beam. When the natural frequencies of the first bending and torsional modes are of the same order of magnitude, we can observe the one-to-one combination resonance in the perturbation analysis depending on the characteristic parameters. The nonlinear behavior about the combination resonance reveals a chaotic motion depending on the natural frequencies and damping ratio. We can analyze the chaotic dynamics by using the eigenvalue analysis of the perturbed components. In this paper, we derived the equations for autonomous system and solved them to obtain the characteristic equation. The stability analysis was carried out by examining the eigenvalues. Numerical integration gave the physical behavior of each mode for given parameters.
Keywords
Combination Resonance; Parametric Excitation; Mathieu Equation; Method of Multiple Scale; Nonlinear Oscillations;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 Yamamoto, T. and Saito, A., 1970, “On the Vibrations of ‘Summed Differential Types’ under Parametric Excitation,” Memories of the Faculty of Engineering, Nagoya University, Vol. 22, No. 1, pp. 54-123.
2 Dugundji, J. and Mukhopadhyay, V., 1973, “Lateral Bending-torsion Vibrations of a Thin Beam under Parametric Excitation,” Journal of Applied Mechanics, Vol. 40, No. 3, pp. 693-698.   DOI
3 Hsu, C. S., 1975, “Limit Cycle Oscillations of Parametrically Excited Second-order Nonlinear Systems,” Journal of Applied Mechanics, Vol. 42, pp. 176-182.   DOI
4 Mukhopadhyay, V., 1980, “Combination Resonance of Parametrically Excited Coupled Second Order Systems with Non-linear Damping,” Journal of Sound and Vibration, Vol. 69, No. 2, pp. 297-307.   DOI
5 Zhang, W., Wang, F. and Yao, M., 2005, “Global Bifurcations and Chaotic Dynamics in Non-linear Non-planar Oscillations of a Parametrically Excited Cantilever Beam,” Nonlinear Dynamics, Vol. 40, No. 3, pp. 251-279.   DOI
6 Cartmell, M. P. and Roberts, J. W., 1988, “Simultaneous Combination Resonances in an Autoparametrically Resonant System,” Journal of Sound and Vibration, Vol. 123, No. 1, pp. 81-101.   DOI
7 Bang, D. J., Lee, G. D., Jo, H. D. and Jeong, T. G., 2008, “Stability of Nonlinear Oscillations of a Thin Cantilever Beam Under Parametric Excitation,” Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 18, No. 2, pp. 160-168.   DOI
8 Bang, D. J., 2007, “Study on the Stability of Nonlinear Oscillations of a Thin Cantilever Beam Under Parametric Excitation,” MS Thesis, Konkuk University, Seoul, Korea.
9 Bolotin, V. V., 1964, “Dynamic Stability of Elastic Systems,” Holden-Day, Inc., San Francisco.