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Reduction of the Residual Vibrations of a Flexible Cantilever Beam Subjected to a Transient Translation or Rotation Motion

Abstract

In this paper, the optimal command input is considered in order to minimize the residual vibrations of a flexible cantilever beam when the beam simply changes its position by translation or rotation. Although a cantilever beam has many modes of vibration, it is shown that the consideration of the first mode is sufficient in this case. Thus, the problem becomes a single-degree-of-freedom system subjected to a ground excitation. Two simple methods are proposed to find the optimal command input based on the shock response spectrum (SRS). The first method is the simplest and can be applied to lightly damped cases, and the second method is applicable to more general problems. The second method gives almost the same results as the input shaping method. However the proposed method gives a easier and clearer control strategy.

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참고문헌 (12)

  1. Diken, H., 2000, 'Vibration Control of a Rotating Euler-Bernoulli Beam', Journal of Sound and Vibration, Vol. 232, No. 3, pp. 541-551 
  2. Kuo, C.-F. J. and Liu, S.-C., 1998, 'Modal Analysis and Control of a Rotating Euler-Bernoulli Beam Part II : Residual Vibration Control', Mathematical and Computer Modelling, Vol. 275, No. 5, pp. 93-97 
  3. Yim, J.-C., Ahn, T.-K. and Cho, J.-K., 2005, 'Reduction of Residual Vibration in Wafer Positioning System Using Input Shaping', Proceedings of the KSNVE Annual Autumn Conference, pp. 559-563 
  4. Sasiadek, J. Z. and Srinivasan, R., 1989, 'Dynamic Modelling and Adaptive Control of a Single-link Flexible Manipulator', Journal of Guidance, Control and Dynamics, Vol. 12, No. 6, pp. 838-844 
  5. Hwang, J.-H., Kong, B.-S. and Lee, S.-C., 1997, 'Robust Input Shaping Controller for Slewing Uncertain Flexible Structures', Proceedings of the KSNVE Annual Spring conference, pp. 316-323 
  6. Kelly, R. D. and Richman, G., 1969, Modeling of the Slewing Control of a Flexible Structure, SVM-5-Principles and Techniques of Shock Data Analysis', Shock and Vibration Information Analysis Center 
  7. Harris, C. M. and Piersol, A. G., 2002, 'Harris' Shock and Vibration Handbook', Fifth Edition, Chapter 8, Transient Response to Step and Pulse Functions, McGraw-Hill 
  8. Park, J. Y. and Chang, P. H., 1994, 'Residual Vibration Control of Robot with Flexible Joints Using Input Shaping ', Transactions of the KSME, Vol. 18, No. 11, pp. 3066-3074 
  9. Garcia, E. and Inman, D. J., 1991, 'Modeling of the Slewing Control of a Flexible Structure', Journal of Guidance, Control and Dynamics, Vol. 14, No. 4, pp. 736-742 
  10. Daafouz, J., Garcia, G. and Bernussou, J., 1998, 'Robust Control of a Flexible Robot Arm Using the Quadratic D-stability Approach', IEEE Transactions on Control Systems Technology, Vol. 6, No. 4, pp. 524-533 
  11. Lee, Y.-S., Elliott, S. J. and Gardonio, P., 2004, 'Active Structural Acoustical Control of a Smart Panel Using Direct Velocity Feedback', Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 14, No. 10, pp. 1007-1014 
  12. Singer, N. C. and Seering, W. P., 1990, 'Pre-shaping Command Inputs to Reduce System Vibration', Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, Vol. 112, pp. 76-82 

이 논문을 인용한 문헌 (1)

  1. Lee, Yunjae ; Kim, Chee-Kyeong ; Choi, Hyun-Chul 2014. "Computational Optimization for RC Columns in Tall Buildings" 콘크리트학회논문집 = Journal of the Korea Concrete Institute, 26(3): 401~409 

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