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Modeling and Verification for Stability Analysis of Axially Oscillating Cantilever Beams

축 방향 왕복운동을 하는 외팔보의 안정성 해석을 위한 모델링 및 검증

  • 김성도 (한양대학교 대학원 기계설계학과) ;
  • 유홍희 (한양대학교 기계공학부)
  • Published : 2006.02.01

Abstract

Modeling and verification for stability analysis of axially oscillating cantilever beams are investigated in this paper Equations of motion for the axially oscillating beams are derived and transformed into dimensionless forms. The equations include harmonically oscillating parameters which are related to the motion-induced stiffness variation. stability diagram is obtained by using the multiple scale perturbation method. To verify the accuracy of the modeling method, several points in the plane of the stability diagram are presented and solved. The present modeling method proves to be as accurate as a nonlinear finite element modeling method.

Keywords

References

  1. Leissa, A., 1981, 'Vibration Aspects of Rotating Turbomachinery Blade,' Applied Mechanics Reviews, Vol.34, pp.629-635
  2. Rao, J., 1987, 'Turbomachine Blade Vibration,' Shock and Vibration Digest, Vol. 19, pp. 3-10
  3. Kane, T., Ryan, R. and Banerjee, A., 1987, 'Dynamics of Cantilever Beam Attached to a Moving Base,' Journal of Guidance, Control, and Dynamics, Vol. 10, pp. 139-151 https://doi.org/10.2514/3.20195
  4. Yoo, H., Ryan, R. and Scott, R., 1995, 'Dynamics of Flexible Beams Undergoing Overall Motion,' J. of Sound of Vibration, Vol. 181, No. 2, pp. 261-278 https://doi.org/10.1006/jsvi.1995.0139
  5. Yoo, H. and Chung, J., 2001, 'Dynamics of Rectangular Plates Undergoing Prescribed Overall Motion,' J. of Sound of Vibration, Vol. 239, No. 1, pp. 123-137 https://doi.org/10.1006/jsvi.2000.3111
  6. Hyun, S. and Yoo, H., 1999, 'Dynamic Modeling and Stability Analysis of Axially Oscillating Cantilever Beams,' J. of Sound of Vibration, Vol. 228, No. 3, pp. 543-558 https://doi.org/10.1006/jsvi.1999.2427
  7. Kim, N., Hyun, S. and Yoo, H., 2003, 'Nonlinear Modeling Employing Hybrid Deformation Variables and Frequency Response Characteristics of a Cantilever Beam Undergoing Axially Oscillating Motion,' Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 13, No. 3, pp. 210-216 https://doi.org/10.5050/KSNVN.2003.13.3.210
  8. Eisenhart, L., 1947, An Introduction to Differential Geometry, Princeton University Press
  9. Kane, T. and Levinson, D., 1985, Dynamics, Theory and Applications, McGraw-Hill Book Co
  10. Nayfeh, A. and Mook, D., 1977, 'Parametric Excitations of Linear Systems Having Many Degree of Freedom,' J. Acoust. Soc. Am., 62, pp. 375-381 https://doi.org/10.1121/1.381535
  11. LS-DYNA 970 Keyword User's Manual, Livermore Software Technology Corp., CA, 2003
  12. LS-DYNA Theoretical Manual, Livermore Software Technology Corp., CA, 2003