Random Vibration of Non-linear System with Multiple Degrees of Freedom

다자유도 비선형계의 불규칙 진동 해석

  • Published : 2006.10.15

Abstract

Vibration of a non-linear system with multiple degrees of freedom under random parametric excitations was evaluated by probabilistic method. The non-linear characteristic terms of system structure were quasi-linearized and excitation terms were remained as they were. An analytical method where the expectation values of square mean of error was minimized was used. The numerical results were compared with those obtained by Monte Carlo simulation. A linear congruential generator and Box-Muller method were used in Monte Carlo simulation. The comparison showed the results by probabilistic method agreed well with those by Monte Carlo simulation.

Keywords

References

  1. Boothroyd, G., 1981, Fundamentals of Metal Machining and Machine Tools, McGraw-Hill
  2. Song, D. Y., Otani, N., Aoki, T., Kamakoshi, Y., Ohara, Y. and Tamaki, H., 2005, 'A new approach to cutting state monitoring in end-mill machining,' Int. J. of Machine Tools & Manuf., Vol. 45, pp. 909-921 https://doi.org/10.1016/j.ijmachtools.2004.10.014
  3. Chen, J. B. and Li, J., 2005, 'Dynamic response and reliability analysis of non-linear stochastic structure,' Probabilistic Engineering Mechanics, Vol. 20, pp. 33-44 https://doi.org/10.1016/j.probengmech.2004.05.006
  4. Jeong, S. H., Cha, K. R. and Ryu, S. H., 1999, 'A Study on the stability of Supervisory Control for Nonlinear System with Saturating Input,' Journal of KSMTE, Vol. 8, No. 4, pp. 112-122
  5. Iwan, W. D. and Huang, C. T., 1996, 'On the dynamic response of non-linear systems with parameter uncertainty,' International Journal of Non-Linear Mechanics, Vol. 31, No. 5, pp. 631-645 https://doi.org/10.1016/0020-7462(96)00027-3
  6. To, C. H. S., 2000, Nonlinear Random Vibration: Analytical Techniques and Applications, Swets & Zeitlinger B.V
  7. Lin, Y. K. and Cai, G. Q., 2004, Probabilistic Structural Dynamics: Advanced Theory and Applications, McGraw-Hill
  8. Elishakoff, I., 1999, Probabilistic Theory of Structures, Dover Publications, Inc
  9. Marek, P., Brozzetti, J., and Gustar, M., 2001, Probabilistic Assessment of Structures using Monte Carlo Simulation, Institute of Theoretical and Applied Mechanics, Praha
  10. Landau, D. P. and Binder, K., 2000, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press
  11. Meirovitch, L., 1985, Introduction to Dynamics and Control, John Wiley & Sons
  12. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T., 1988, Numerical Recipes in C, Cambridge University Press