Journal of KSNVE (소음진동)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
권호 표지

Comparison Between Two Analytical Solutions for Random Vibration Responses of a Spring-Pendulum System with Internal Resonance

내부공진을 가진 탄성진자계의 불규칙 진동응답을 위한 두 해석해의 비교

  • 조덕상 (한국전력기술(주) 원자로설계개발단) ;
  • 이원경 (영남대학교 기계공학부)
  • Published : 1998.08.01
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Abstract

An investigation into the stochastic bifurcation and response statistics of an autoparameteric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to genrage a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinanary differential equations. In view of equilibrium solutions of this system and their stability we examine the stochastic bifurcation and response statistics. The analytical results are compared with results obtained by Monte Carlo simulation.

Keywords

References

  1. Journal of Sound and Vibration v.44 no.3 Broad Band Random Excitation of a Two-Degree-of-Freedom System with Autoparametric Coupling Ibrahim, R. A.;Roberts, J. W.
  2. ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design v.108 Autoparametric Vibration of Coupled Beams Under Random Support Motion Ibrahim, R. A.;Heo, H.
  3. Journal of Sound and Vibration v.123 no.3 Structural Modal Interaction with Combination Internal Resonance under Wide-Band Random Excitation Ibrahim, R. A.;Li, W.
  4. Journal of Sound and Vibration v.69 no.1 Random Excitation of a Vibratory System with Autoparametric Interaction Roberts, J. W.
  5. ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design v.117 Recent Results in Random Vibrations of Nonlinear Mechanical Systems Ibrahim, R. A.
  6. 한국소음진동공학회지 v.8 no.3 광대역 불규칙가진력을 받는 탄성진자계의 내부공진효과 이원경;조덕상
  7. ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design v.115 Structural Modal Multifurcation With Internal Resonance-Part 2 : Stochastic Approach Ibrahim, R. A.;Lee, B. H.;Afaneh, A. A.
  8. Probabilistic Engineering Mechanics v.9 Stochastic Bifurcation in Non-linear Structural Systems near 1:1 Internal Resonance Lee, B. H.;Ibrahim, R. A.
  9. Nonlinear Dynamics v.8 Parametric Random Excitation of Nonlinear Coupled Oscillators Yoon, Y. J.;Ibrahim, R. A.
  10. ASME Journal of Applied Mechanics v.54 Cumulant-Neglect Closure Method for Nonlinear Systems under Random Excitations Sun, J. Q.;Hsu, C. S.
  11. International Journal of Non-Linear Mechanics v.17 An Exact Solution to a Certain Nonlinear Random Vibration Problem Dimenberg, M. F.
  12. Journal of Sound and Vibration v.171 no.3 A Global Analysis of an Harmonically Excited Spring-Pendulum System with Internal Resonance Lee, W. K.;Hsu, C. S.
  13. Nonlinear Dynamics v.14 Chaotic Dynamics of a Harmonically Excited Spring-Pendulum System with Internal Resonance Lee, W. K.;Park, H. D.
  14. Random Differential Equations in Science and Engineering Soong, T. T.
  15. Parametric Random Vibration Ibrahim, R. A.
  16. Probabilistic Theory of Structural Dynamics Lin, Y. K.
  17. Applied Mechanics Review v.44 Simulation of Stochastic Processes by Spectral Representation Shinozuka, M.;Deodatis, G.
  18. Random Vibration of Structures Yang, C. Y.