Browse > Article
http://dx.doi.org/10.5050/KSNVN.2009.19.6.591

Extension of Rational Interpolation Functions for FE Analysis of Rotating Beams  

Kim, Yong-Woo (순천대학교 기계공학과)
Jeong, Jae-Ho (순천대학교 대학원 기계공학과)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.19, no.6, 2009 , pp. 591-598 More about this Journal
Abstract
Starting from the rotating beam finite element in which the interpolating shape functions satisfy the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfy the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beams.
Keywords
Rotating Beam; Rational Interpolation Function; Finite Element Method; Euler-Bernoulli Beam; Hermitian Shape Function;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Banerhee, J. R., 2000, “Free Vibration of Centrifugally Stiffened Uniform and Tapered Beams Using the Dynamic Stiffness Method,” Journal of Sound and Vibration, Vol. 233, No. 5, pp. 857-875   DOI   ScienceOn
2 Hodges, D. J. and Rutkowski, M. J., 1981, “Free Vibration Analysis of Rotating Beams by a Variable order Finite Element Method,” AIAA Journal, Vol. 19, No. 11, pp. 1459-1466   DOI   ScienceOn
3 Yokoyama, T., 1988, “Free Vibration Characteristics of Rotating Timoshenko Beams,” International Journal of Mechanical Sciences, Vol. 30, No. 10, pp. 743-755   DOI   ScienceOn
4 Wang, G. and Wereley N. M., 2004, “Free Vibration Analysis of Rotating Blades with Uniform Tapers,” AIAA Journal, Vol. 42, No. 12, pp. 2429-2437   DOI   ScienceOn
5 Chakraborty, A., Gopalakrishnan, S. and Reddy, J. N., 2003, “A New Finite Element for the Analysis of Functionally Graded Materials,” International Journal of Mechanical Sciences, Vol. 45, pp. 519-539   DOI   ScienceOn
6 Gunda, J. B. and Ganguli, R., 2008, “New Rational Interpolation Functions for Finite Element Analysis of Rotating Beams, International Journal of Mechanical Sciences,” Vol. 50, pp. 578-588   DOI   ScienceOn
7 Ozgumus, O. O. and Kaya, M. O., 2007, “Energy Expressions and Free Vibration Analysis of a Rotating Double Tapered Timoshenko Beam Featuring Bending-Torsion Coupling,” International Journal of Engineering Science, Vol. 45, pp. 562-586   DOI   ScienceOn
8 Yoo, H. H. and Shin, S. H., 1998, “Vibration Analysis of Rotating Cantilever Beams,” Journal of Sound and Vibration, Vol. 212, No. 5, pp. 807-828   DOI   ScienceOn
9 Giurgiutiu, V. and Stafford, R. O., 1977, “Semianalytic Methods for Frequencies and Mode Shapes of Rotor Blades,” Veritica, Vol. 1, No. 4, pp. 291-306