DOI QR코드

DOI QR Code

축 방향 가속을 받는 보 구조물의 동적 안정성 해석

Dynamic Stability Analysis of an Axially Accelerating Beam Structure

  • 은성진 (한양대학교 대학원 기계설계학과) ;
  • 유홍희 (한양대학교 공과대학 기계공학부)
  • 발행 : 2005.09.01

초록

Dynamic stability of an axially accelerating beam structure is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively large unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

키워드

참고문헌

  1. Kane, T. B., Ryan, R. and Banerjee, A., 1987, 'Dynamics of Cantilever Beam Attached to a Moving Base,' Journal of Guidance, Control, and Dynamics, 10, pp. 139-151 https://doi.org/10.2514/3.20195
  2. Yoo, H. H., Ryan, R. R. and Scott, R. A., 1995, 'Dynamics of Flexible Beams Undergoing Overall Motions,' J. of Sound and Vibration, Vol. 181, No. 2, pp. 261-278 https://doi.org/10.1006/jsvi.1995.0139
  3. Leonard Meiroviteh, 1970, Methods of Analytical Dynamics, Mcgraw-Hill
  4. Nayfeh, A. and Mook, D., 1979, Nonlinear Oscillation, John Wiley & Sons, Inc
  5. Hyun, S. and Yoo, H., 1999, 'Dynamic Modeling and Stability Analysis of Axially Oscillating Cantilever Beams,' J. of Sound and Vibration, Vol. 228, No. 3, pp. 543-558 https://doi.org/10.1006/jsvi.1999.2427
  6. Hyun, S. and Yoo, H., 'Dynamic Modeling and Stability Analysis of a Flying Structure Undertaking Parametric Excitation Forces,' Transactions of the KSNVE, Vol. 9, No. 6, pp. 1157-1165
  7. Faraday, M., 1831, 'On a Peculiar Class of Acoustical Figures and on Certain Forms Assumed by a Group of Particles upon Vibrating Elastic Surfaces,' Phil. Trans. Ray. Soc. (London), pp. 299-318
  8. Mathiu, E., 1868, 'Memoire sur le Movement Vibratoire d'une Membrane de Forme Elliptique,'J. Math., 13, pp. 137-203
  9. Hill, G., 1886, 'on the Part of the Lunar Perigee which is a Function of the Mean Motions of the Sun and Moon,' Acta Math., 8, pp. 1-36 https://doi.org/10.1007/BF02417081
  10. Floquet, G., 1883, 'Sur les Equation Differentielles Lineaires a Coefficients Periodique,' Annales de Ecole Normal Superior, Paris, Vol. 2, No. 12, pp. 47-89
  11. Beal, T., 1965, 'Dynamic Stability of a Flexible Missile under Constant and Pulsating Thrusts,' AIAA J., 3, pp. 486-494 https://doi.org/10.2514/3.2891
  12. Iwatsubo, T., Saigo, M. and Sugiyama, Y., 1973, 'Parametric Instability of Clamped-clamped and Clamped Simply Supported Columns Under Periodic Axial Loads,'J. of Sound and Vibration, 30, pp. 65-77 https://doi.org/10.1016/S0022-460X(73)80050-1
  13. Nayfeh, A. and Mook, D., 1977, 'Parametric Excitatioins of Linear Systems Having Many Degrees of Freedom,' J. Acoust. Soc. Am., 62, pp. 375-381 https://doi.org/10.1121/1.381535