Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Nonlinear Responses of a Hinged-Clamped Beam under Random Excitation

불규칙 가진되는 회전-고정보의 비선형응답특성

  • 조덕상 (영남대학교 공업기술연구소) ;
  • 김영종 (상주대학교 기계공학부)
  • Published : 2000.12.01
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Abstract

This study presents the nonlinear responses of a hinged-clamped beam under broadband random excitation. By using Galerkin's method the governing equation is reduced to a system or nonautonomous nonlinear ordinary differential equations. The Fokker-Planck equation is used to generate a general first-order differential equation in the joint moments of response coordinates. Gaussian and non-Gaussian closure schemes are used to close the infinite coupled moment equations. The closed equations are then solved for response statistics in terms of system and excitation parameters. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. Monte Carlo simulation is used for numerical verification.

이 논문은 불규칙 가진력을 받는 회전-고정보의 비선형 응답특성을 나타낸다. 불규칙 가진력은 두 번째 고유모드의 절점과 최대변위점에 가했다. 비선형 편미분 방정식과 경계조건으로 표현되는 이 문제를 Galerkin의 방법을 이용하여 연립 비선형 상미분방정식으로 변환하였다. 이 상미분방정식으로부터 Fokker-Planck방정식과 모멘트 방정식을 얻은 후 Gaussian closure 방법 및 non-Gaussian closure 방법을 이용하여 3 모드 근사시 각각 27개 및 209개의 자율 상미분방정식을 구하였다. Gaussian closure 방법과 non-Gaussian closure 방법으로 2 모드 및 3 모드 근사해석을 수행하였고 해석적 결과들은 Monte Carlo 시뮬레이션 결과와 비교되었다. 해석결과 2 모드 근사해와 3 모드 근사해가 거의 일치하였고 2 모드 내부공진만 고려하여도 해석결과에 별 영향을 주지 않는다는 것을 알 수 있다.

Keywords

References

  1. Transactions of the ASME, Journal of Applied Mechanics v.37 Non-linear Vibrations of Beam under Harmonic Excitation W.Y.Tseng;J.Dugundji
  2. Transactions of the ASME, Journal of Applied Mechanics v.40 Nonlinear Vibrations of a Hinged Beam including Nonlinear Inertia Effects S.Atluri
  3. Transactions of the ASME, Journal of Applied Mechanics v.42 Nonlinear Vibration of Beams Using a Form-Function Approximation C.L.Lou;D.L.Sikarskie
  4. Journal of Sound and Vibration v.114 no.1 Application of the Ritz method to the Analysis of Nonlinear Free Vibration of Beams R.Lewandowski
  5. Journal of Acoustical Society of America v.55 no.2 Nonlinear Analysis of the Forced Response of Structural Elements A.H.Nayfeh;D.T.Mook;S.Sridhar
  6. Journal of Acoustical Society of America v.58 no.1 Nonlinear Resonances in a Class of Multi-Degree-of-Freedom Systems S.Sridhar;A.H.Nayfeh;D.T.Mook
  7. Nonlinear Oscillations A.H.Nayfeh;D.T.Mook
  8. Nonlinear Dynamics v.6 Nonlinear Analysis of the Forced Response of a Beam with Three Mode Interaction W.K.Lee;K.Y.Soh
  9. Transactions of the ASME, Journal of Applied Mechanics v.61 Domains of Attraction of a Forced Beam by Interpolated Mapping W.K.Lee;M.R.Ghang
  10. Nonlinear Dynamics v.14 Evolution of Domains of Attraction of a Foreced Beam with Two-Mode Interaction W.K.Lee;C.H.Kim
  11. Transactions of the ASME, Journal of Vibration Acoustics, Stress and Reliability in Design v.115 Structural Modal Multifurcation With Internal Resonance-Part 2: Stochastic Approach R.A.Ibrahim;B.H.Lee;A.A.Afaneh
  12. Probabilistic Engineering Mechanics v.9 Stochastic Bifurcation in Non-linear Structural Systems near 1:1 Internal Resonance B.H.Lee;R.A.Ibrahim
  13. Random Differential Equations in Science and Engineering T.T.Soong
  14. Parametric Random Vibration R.A.Ibrahim
  15. Probabilistic Structural Dynamics Advanced Theory and Application Y.K.Lin;G.Q.Cai
  16. Applied Mechanics Review v.44 Simulation of Stochastic Processes by Spectral Representation M.Shinozuka;G.Deodatis
  17. Random Vibration of Structures C.Y.Yang