Browse > Article
http://dx.doi.org/10.5050/KSNVN.2005.15.7.851

One to One Resonance on the Quadrangle Cantilever Beam  

Kim, Myoung-Gu (인하대학교 기계공학과)
Pak, Chul-Hui (인하대학교 기계공학과)
Cho, Chong-Du (인하대학교 기계공학과)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.15, no.7, 2005 , pp. 851-858 More about this Journal
Abstract
The response characteristics of one to one resonance on the quadrangle cantilever beam in which basic harmonic excitations are applied by nonlinear coupled differential-integral equations are studied. This equations have 3-dimensional non-linearity of nonlinear inertia and nonlinear curvature. Galerkin and multi scale methods are used for theoretical approach to one-to-one internal resonance. Nonlinear response characteristics of 1st, 2nd, 3rd modes are measured from the experiment for basic harmonic excitation. From the experimental result, geometrical terms of non-linearity display light spring effect and these terms play an important role in the response characteristics of low frequency modes. Nonlinear nitration in the out of plane are also studied.
Keywords
Non-linear Coupling; Planar Motion; Non-planar Motion; Jump Phenomenon; Flexible Structures; Internal Resonance; One-to-one Resonance;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 김명구, 박철희, 조종두, 박창호, 2004, '얇은 직사각형 외팔보의 비선형 진동현상,' 한국소음진동공학회논문집, 제 14 권, 제 12 호, pp.1314-1321   DOI
2 Haddow, A. G. and Barr, A. D. S. and Mook, D. T., 1984, Theoretical and Experimental Study of Modal Interaction in a Two-degree-offreedom Structure, Journal of Sound and Vibration, Vol. 97, pp.451-473   DOI   ScienceOn
3 Zaretzky, C. L. and Crespo da silva, M. R. M.. 1994, Experimental Investigation of Non-linear Modal Coupling in the Response of Cantilever Beans, Journal of Sound and Vibration, Vol. 174, pp.145-167   DOI   ScienceOn
4 Brach. J. T., 1975, Non-linear Amplitude Distortion in Vibrating System, Bruel and Kjaer, pp.52-82
5 Crespo da silva, M. R. M. and Glynn, C. C., 1978. 'Nonlinear Flexural-flexural-torsional Dynamics of Inextensional Beams. II. Forced Motions'. J. Struct. Mech., Vol. 6. pp. 449-461   DOI   ScienceOn
6 정구충, 임재훈, 최연선 2004, 부가질량을 갖는 구속외팔송수관의 비선형 동특성, 한국소음진동공학회논문집, 제 14권, 제 7호. pp. 561-568
7 Lee, W. K. and Park, H. D.. 1997, 'Chaotic Dynamics of a Harmonically Excited SpringPendulum System with Internal Resonance, Nonlinear Dynamics', Vol. 34, No.4, pp.749-757
8 김명구, 박철희, 조종두, 이흥식, 2005, '사각형 외팔보에서의 일대일 공진,' 한국소음진동공학회춘계학술대회논문집, pp.424-429
9 Haight, E. C. and King, W. W., 1971, Stability of Non-linear Oscillations of an Elastic Rod, Journal of the Acoustical Society of America., Vol. 52, pp.899-911   DOI
10 Zavodney, L. D. and Navfeh, A. H., 1989, The Nonlinear Response of a Slender Beam Carrying a Lumped Mass to a Principal Parametric Excitation :Theory and Experiment, International Journal of Nonlinear Mechanics, Vol. 24, pp.105-125   DOI   ScienceOn
11 Perngjin F. Pai and Ali H. Nayfeh . 1990, 'Non-linear Non-planar Oscillations of a Cantilever Beam Under Lateral Base Excitations', Int. J. Non-linear Mechanics, Vol. 25, No. 5, .pp. 455-474   DOI   ScienceOn
12 Tseng, W. Y. and Dugundji, J., 1970, 'Nonlinear Vibrations of a Beam Under Harmonic Excitation', Journal of Applied Mechanics. Vol. 37, pp.292-297   DOI
13 Ali H. Nayfeh and Perngjin F. Pai, 1989. Non-linear Non-planar Parametric Responses of an Inextensional Beam, J. Non-linear Mechanics', Vol. 24, No.2, pp. 139 - 158   DOI   ScienceOn
14 Ali H. Nayfeh 2000. Nonlinear Interactions Analytical, Computational and Experimental Methods, pp.181 -345
15 Randall, R. B., B. Tch., B. A. 1987, Frequency Analysis. pp.265-267