Browse > Article
http://dx.doi.org/10.5050/KSNVE.2010.20.11.1058

Vibration Analysis of a Rotating Cantilever Beam with Tip Mass Using DTM  

Kim, Min-Ju (경북대학교 대학원 기계공학부)
Kang, Nam-Cheol (경북대학교 기계공학부)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.20, no.11, 2010 , pp. 1058-1063 More about this Journal
Abstract
The vibration analysis of a rotating cantilever beam with tip mass was studied by using DTM(differential transformation method). DTM is one of the numerical methods, for finding series solutions by transforming differential equations to algebraic ones similar with Laplace transform. The advantages of the DTM are that it is easy to understand and is effective in finding numerical solutions. Applying DTM, the natural frequencies of a rotating cantilever beam were obtained taking into consideration the effects of tip mass. Also, convergence study of DTM was performed to decide the number of terms used in eigenvalue problems. Numerical results obtained by DTM show good agreement with those by other methods. As a result, it is expected that DTM can be a useful method in vibration analysis such as that of a rotating cantilever beam with tip mass.
Keywords
Differential Transformation Method; Rotating Cantilever Beam; Tip Mass; Vibration Analysis; Convergence;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Southwell, R. V. and Gough, B. S., 1921, “On the Free Transverse Vibrations of Airscrew Blades,” British A. R. C Reports and Memoranda, No. 766.
2 Lee, J. H. and Yoo, H. H., 2009, “Vibration Analysis of Tip Mass Cantilever Beam Having Tapered Cross Section,” Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 19, No. 4, pp. 363-369.   DOI
3 Bhat, R. B., 1986, “Transverse Vibrations of a Rotating Uniform Cantilever Beam with Tip Mass as Predicted by Using Beam Characteristic Orthogonal Polynomials in the Rayleigh-Ritz Method,” Journal of Sound and Vibration, Vol. 105, No. 2, pp. 199-210.   DOI
4 Hoa, S. V., 1979, “Vibration of a Rotating Beam with Tip Mass,” Journal of Sound and Vibration, Vol. 67, No. 3, pp. 369-381.   DOI   ScienceOn
5 Yoo, H. H., 1994, “Dynamic Analysis of Tip Mass Cantilever Beam Undergoing Rigid Body Motion,” Journal of the Korean Society for Aeronautical & Space Sciences, Vol. 22, No. 6, pp. 86-91.
6 Chen, C. and Chen, S., 2004, “Application of the Differential Transformation Method to a Non-linear Conservative System,” Mathematics and Computation, Vol. 154, No. 2, pp. 431-441.   DOI
7 Meirovitch, L., 2001, Fundamentals of Vibrations, McGraw-Hill Companies, Inc., NewYork.
8 Wright, A. D., Smith, C. E., Thresher, R. W. and Wang, J. L. C., 1982, “Vibration Modes of Centrifugally Stiffened Beams,” Journal of Applied Mechanics, Vol. 49, pp. 197-202.   DOI
9 Zhou, J. K., 1986, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan China(In Chinese).
10 $\ddot{O}zdemir, ddot{O}$. and Kaya, M. O., 2006, “Flapwise Bending Vibration Analysis of a Rotating Tapered Cantilever Bernoulli-Euler Beam by Differential Transform Method,” Journal of Sound and Vibration, Vol. 289, pp. 413-420.   DOI