Dynamic Stability of a Free-Free Beam with a Tip Rigid Body under a Controlled Pulsating Thrust

끝단 강체를 갖고 맥동 제어추력을 받는 양단 자유보의 동적 안정성

  • Published : 2000.01.01


The paper describes the parametric instability of free-free beams subjected to a controlled pulsating follower force. The beam has a tip rigid body not a mass point, and the direction of pulsating follower force is controlled by the direction control sensor. Equations of motion are derived by Hamilton's principle and the instability regions are obtained by finite element formulation. The effects of magnitude, rotary inertia, the distance between free end of the beam and the center of gravity of the rigid body on the instability types and regions are investigated by the change of the constant and periodic part of the follower force.


Tip Rigid Body;Pulsating Controlled Thrust;Free-Free Beam;Parametric Instability


  1. Kim, J. H. and Choo, Y. S., 1998, 'Dynamic Stability of a Free-Free Timoshenko Beam Subjected to a Pulsating Follower Force,' Journal of Sound and Vibration, Vol. 216, pp. 623-636
  2. Chen, S. H., Liu, Z. H., Han, W. Z. and Ma, A. J., 1994, 'Determining Free-Free Models from Experimental Data of Constrained Structures,' AIAA Journal, Vol. 32, pp. 440-443
  3. Sugiyama, Y., Matsuike, J., Ryu, B. J., Katayama, K., Kinoi, K. and Enomoto, N., 1995, 'Effect of Concentrated Mass on Stability of Cantilevers under Rocket Thrust,' AIAA Journal, Vol. 33, pp. 499-503
  4. Mladenov, K. A. and Sugiyama, Y., 1997, 'Stability of a Jointed Free-Free Beam under End Rocket Thrust,' Journal of Sound and Vibration, Vol. 199, pp. 1-15
  5. Park, Y. P. and Mote Jr, C. D., 1985, 'The Maximum Controlled Follower Force on a Free-Free Beam Carring a Concentrated Mass,' Journal of Sound and Vibration, Vol. 98, pp. 247-256
  6. Park, Y. P. and Ryu, B. J., 1987, 'Effect of a Concentrated Mass on the Stability of a Free Timoshenko Beam under a Controlled Follower Force,' Proceedings of the KSME/JSME Vibration Conference, pp. 309-318
  7. Sugiyama, Y., Katayama, T., Fukuda, H. and Kar, C., 1989, 'Effect of Internal Damping on the Stability of Free-Free Beams under an End Thrust(in Japanese),' Transactions of the JSME, Vol. 55, pp. 243-247
  8. Hsu, C. S., 1963, 'On the Parametric Excitation of a Dynamic System Having Multiple Degrees of Freedom,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 30, pp. 367-372
  9. Wu, J. J., 1975, 'On the Stability of a Free-Free Beam under Axial Thrust Subjected to Directional Control,' Journal of Sound and Vibration, Vol. 42, pp. 45-52
  10. Wu J. J., 1976, 'Missile Stability using Finite Elements-An Unconstrainted Variational Approach,' AIM Journal, Vol. 14, pp. 313-319
  11. Beal, T. B., 1965, 'Dynamic Stability of a Flexible Missile under Constant and Pulsating Thrusts,' AIAA Journal, Vol. 3, pp. 486-494