A Finite Element Analysis for a Rotating Cantilever Beam

회전 외팔보의 유한요소 해석

  • Jeong, Jin-Tae (Department of Mechanical Engineering, College of Engineering, Hanyang University) ;
  • Yu, Hong-Hui (Department of Mechanical Engineering, College of Engineering, Hanyang University) ;
  • Kim, Gang-Seong
  • Published : 2001.11.01


A finite element analysis for a rotating cantilever beam is presented in this study. Based on a dynamic modeling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are (derived from Hamilton's principle. Two of the linear differential equations show the coupling effect between stretch and chordwise deformations. The other equation is an uncoupled one for the flapwise deformation. From these partial differential equations and the associated boundary conditions, two weak forms are derived: one is for the chordwise motion and the other is fur the flptwise motion. The weak farms are spatially discretized with newly defined two-node beam elements. With the discretized equations or the matrix-vector equations, the behaviors of the natural frequencies are investigated for the variation of the rotating speed.


Rotating Cantilever Beam;Stretch Deformation;Finite Element Method;Natural Frequency Variation


  1. Kane, T. R., Ryne, R. R., and Banerjee, A. K., 1987, 'Dynamics of a Cantilever Beam Attached to a Moving Base,' Journal of Guidance, Control, and Dynamics, Vol. 10, pp. 139-151
  2. Chung, J. and Hulbert, G. M., 1993, 'A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation : the Generalized-${\alpha}$ Method,' ASME Journal of Applied Mechanics, Vol. 60, pp. 371-375
  3. Christensen, E. and Lee, S., 1986, 'Non-Linear Finite Element Modelling of the Dynamic System of Unrestrained Flexible Stuctures,' Computer & Structures, Vol. 23, pp. 819-829
  4. Yoo, H. H., Ryan, R. R., and Scott, R.,A., 1995, 'Dynamics of Flexible Beams Undergoing Overall Motion,' Journal of Sound and Vibration, Vol. 181, pp. 261-278
  5. Simo, J. and Vu-Quoc, L., 1987, 'On the Dynamics of Flexible Beams Under Large Overall Motions-the Plane Case : Part I and Part II,' ASME Journal of Applied Mechanics, Vol. 53, pp. 849-863
  6. Belytschko, T. and Hsieh, B., 1973, 'Non-Linear Transient Finite Element Analysis with convected Coordiantes,' International Journal for Numerical Methods in Engineering, Vol. 7, pp. 255-271
  7. Bodley, C., Dever, A., Park, A., and Frisch, A., 1978, 'A Digital Computer Program for the Dynamic Interaction Simulation of Controls and Structure,' NASA TP-1219
  8. Hfisch, H., 1975, 'A Vector-Dyadic Development of the Equations of Motion for N-Couloed Flexible Bodies and Point Masses,' NASA TN D-8047
  9. Ho, J., 1977, 'Direct Path Mathod for Flexible Multibody Spacecraft Dynamics,' Journal of Spacecraft and Rockets, Vol. 14, pp. 102-110
  10. 유홍회, 1992, '회전 외팔보의 굽힘 진동해석,' 대한기계학회논문집, 제16권, 제5호, pp. 891-3898
  11. Yoo, H. H. and Shin, S. H., 1998, 'Vibration Analysis of Rotating Cantilever Beams,' Journal of Sound and Vibration, Vol. 212, pp. 807-828
  12. Putter, S. and Manor, H., 1978, 'Natural Frequencies of Radial Rotating Beams,' Journal of Sound and Vibration, Vol. 56, pp. 175-185
  13. Bauer, H.F., 1980, 'Vibration of a Rotating Uniform Beam,' Journal of Sound and Vibration, Vol. 72, pp. 177-189
  14. Schilhansl, M., 1958, 'Bending Frequency of a Rotating Cantilever Beam,' ASME Journal of Applied Mechanics, Vol. 25, pp. 28-30
  15. Southwell,R. and Gough,F., 1921, 'The Free Transverse Vibratioin of Airscrew Blades,' British A.R.C. Reports and Memeranda, No. 766