Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (12): 1389-1393.

• 论文 • 上一篇    下一篇

MODELING AND BIFURCATION ANALYSIS OF THE CENTRE RIGID-BODY MOUNTED ON AN EXTERNAL TIMOSHENKO BEAM

肖世富1, 陈滨2   

  1. 1. Southwest Institute of Structural Mechanics, Chengdu 610003, P. R. China;
    2. Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China
  • 收稿日期:1997-06-17 修回日期:1999-04-19 出版日期:1999-12-18 发布日期:1999-12-18
  • 基金资助:
    the National Natural Science Foundation(19332022);863 Hi-Tech Project (863-2-2-4-2)

MODELING AND BIFURCATION ANALYSIS OF THE CENTRE RIGID-BODY MOUNTED ON AN EXTERNAL TIMOSHENKO BEAM

Xiao Shifu1, Chen Bin2   

  1. 1. Southwest Institute of Structural Mechanics, Chengdu 610003, P. R. China;
    2. Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China
  • Received:1997-06-17 Revised:1999-04-19 Online:1999-12-18 Published:1999-12-18
  • Supported by:
    the National Natural Science Foundation(19332022);863 Hi-Tech Project (863-2-2-4-2)

摘要: For the system of the centre rigid-body mounted on an external cantilever beam,the equilibrium solution of the steadily rotatin g beam is stable if th e effect of its shearing stress(i.e.the beam belongs to the Euler-Bernoulli type)is not considered.But for the deep beam,it is necessary to con sider the effect of the shearing stress(i.e.the beam belongs to the Timoshenko type).In this case,the ten sion buckling of the equilibrium solution of th e steadily rotating beam may occur. In the present work,usin g the general Hamilton Variation Principle,a nonlinear dynamic model of th e rigid-flexible system with a centre rigid-body mounted on an external Timoshenko beam is established.The bifurcation regular of the steadily rotatin g Timoshenko beam is investigated by using numerical methods.Furthermore, the critical rotating velocity is also obtained.

Abstract: For the system of the centre rigid-body mounted on an external cantilever beam,the equilibrium solution of the steadily rotatin g beam is stable if th e effect of its shearing stress(i.e.the beam belongs to the Euler-Bernoulli type)is not considered.But for the deep beam,it is necessary to con sider the effect of the shearing stress(i.e.the beam belongs to the Timoshenko type).In this case,the ten sion buckling of the equilibrium solution of th e steadily rotating beam may occur. In the present work,usin g the general Hamilton Variation Principle,a nonlinear dynamic model of th e rigid-flexible system with a centre rigid-body mounted on an external Timoshenko beam is established.The bifurcation regular of the steadily rotatin g Timoshenko beam is investigated by using numerical methods.Furthermore, the critical rotating velocity is also obtained.

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