XIAO Shi-fu, CHEN Hong-yong, NIU Hong-pan. Locally Confined Buckling Analysis of Self-Rotating Cantilever Beams[J]. Applied Mathematics and Mechanics, 2016, 37(2): 138-148. doi: 10.3879/j.issn.1000-0887.2016.02.003
Citation: XIAO Shi-fu, CHEN Hong-yong, NIU Hong-pan. Locally Confined Buckling Analysis of Self-Rotating Cantilever Beams[J]. Applied Mathematics and Mechanics, 2016, 37(2): 138-148. doi: 10.3879/j.issn.1000-0887.2016.02.003

Locally Confined Buckling Analysis of Self-Rotating Cantilever Beams

doi: 10.3879/j.issn.1000-0887.2016.02.003
Funds:  The National Natural Science Foundation of China(11402244)
  • Received Date: 2015-08-23
  • Rev Recd Date: 2015-10-15
  • Publish Date: 2016-02-15
  • The nonlinear model of a self-rotating cantilever beam confined by a restrictor located at an arbitrary position along the beam, was established. The stability of the system was investigated with the Ritz method. For the restrictor without friction, the critical values related to the restrictor’s position of the system losing its stability, the bifurcation modes, the post-buckling solutions and the optimal position of the stabilizing restrictor were obtained. Then the analytical critical values and the optimal position were numerically verified with the finite element method. The results obtained with the 2 methods were consistent with each other. Furthermore, the influences on the system stability by the frictions caused by the clamping force and the supporting force from the restrictor were studied. The investigation shows that a critical value of the rotational velocity exists for the self-rotating cantilever beam locally confined by a restrictor. After the rotational velocity exceeds the critical value, the trivial equilibrium loses its stability through the pitchfork bifurcation. While the rotational velocity recovers from the buckling state, significant hysteresis occurs due to the friction caused by the clamping force of restriction, and the buckling system comes back to the trivial equilibrium with a rotational velocity lower than the critical value. The optimal position of the stabilizing restrictor is located at about 78% of the beam length from the cantilever fixed end. These results are useful to guide the restrictor installation.
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  • [1]
    Godoy L A, Mirasso A E. On the elastic stability of static non-holonomic systems[J]. International Journal of Solids and Structures,2003,40(13/14): 3439-3462.
    [2]
    Chateau X, Nguyen Q S. Buckling of elastic structures in unilateral contact with or without friction[J]. European Journal of Mechanics—A/Solids,1991,10(1): 71-89.
    [3]
    Domokos G, Holmes P, Royce B. Constrained Euler buckling[J]. Journal of Nonlinear Science,1997,7(3): 281-314.
    [4]
    Chai H. The post-buckling response of a bi-laterally constrained column[J]. Journal of the Mechanics and Physics of Solids,1998,46(7): 1155-1181.
    [5]
    Holmes P, Domokos G, Schmitt J, Szeberényi I. Constrained Euler buckling: an interplay of computation and analysis[J]. Computer Methods in Applied Mechanics and Engineering,1999,170(3/4): 175-207.
    [6]
    郭英涛, 任文敏. 关于限制失稳的研究进展[J]. 力学进展, 2004,34(1): 41-52.(GUO Ying-tao, REN Wen-min. Some advances in confined buckling[J]. Advances in Mechanics,2004,34(1): 41-52.(in Chinese))
    [7]
    武秀根, 郑百林, 贺鹏飞. 限制失稳模态方程及约束载荷计算[J]. 应用力学学报, 2009,26(2): 375-378.(WU Xiu-gen, ZHENG Bai-lin, HE Peng-fei. Constrained buckling equations and reaction load of bar[J]. Chinese Journal of Applied Mechanics,2009,26(2): 375-378.(in Chinese))
    [8]
    Chen J S, Fang J. Deformation sequence of a constrained spatial buckled beam under edge thrust[J]. International Journal of Non-Linear Mechanics,2013,55: 98-101.
    [9]
    Tzaros K, Mistakidis E. The constrained buckling problem of geometrically imperfect beams: a mathematical approach for the determination of the critical instability points[J]. Meccanica,2015,50(5): 1263-1284.
    [10]
    Katz S, Givli S. The post-buckling behavior of a beam constrained by springy walls[J]. Journal of the Mechanics and Physics of Solids,2015,78: 443-466.
    [11]
    Kane T R, Ryan R R, Banerjee A K. Dynamics of a cantilever beam attached to a moving base[J]. Journal of Guidance, Control, and Dynamics,1987,10(2): 139-151.
    [12]
    Bloch A M. Stability analysis of a rotating flexible system[J]. Acta Applicandae Mathematica,1989,15(3): 211-234.
    [13]
    Lee S Y, Kuo Y H. Bending frequency of a rotating beam with an elastically restrained root[J]. Journal of Applied Mechanics,1991,58(1): 209-214.
    [14]
    Haering W J, Ryan R R. New formulation for flexible beams undergoing large overall plane motion[J]. Journal of Guidance, Control, and Dynamics,1994,17(1): 76-83.
    [15]
    肖世富, 陈滨. 中心刚体-外Timoshenko梁系统的建模与分岔特性研究[J]. 应用数学和力学, 1999,20(12): 1286-1290.(XIAO Shi-fu, CHEN Bin. Modeling and bifurcation analysis of the centre rigid-body mounted on an external Timoshenko beam[J]. Applied Mathematics and Mechanics,1999,20(12): 1286-1290.(in Chinese))
    [16]
    肖世富, 陈滨. 离心场中纵向悬臂梁的大范围分岔分析[J]. 力学学报, 2000,32(5): 559-565.(XIAO Shi-fu, CHEN Bin. Global bifurcation analysis of a cantilever beam vertically fixed in centrifugal field[J]. Acta Mechanica Sinica,2000,32(5): 559-565.(in Chinese))
    [17]
    XIAO Shi-fu, CHEN Bin, DU Qiang. On dynamic behavior of a cantilever beam with tip mass in a centrifugal field[J]. Mechanics Based Design of Structures and Machines: An International Journal,2005,33(1): 79-98.
    [18]
    Xiao S F, Chen B. Dynamic characteristic and stability analysis of a beam mounted on a moving rigid body[J]. Archive of Applied Mechanics,2005,74(5/6): 415-426.
    [19]
    XIAO Shi-fu, CHEN Bin, YANG Min. Bifurcation and buckling analysis of a unilaterally confined self-rotating cantilever beam[J]. Acta Mechanica Sinica,2006,22(2): 177-184.
    [20]
    Xiao S F, Yang M. Nonlinear dynamic modeling, instability and post-buckling analysis of a rotating beam with a flexible support[J]. International Journal of Structural Stability and Dynamics,2006,6(4): 475-491.
    [21]
    肖世富, 许茂. 轴对称转动粘弹性简支梁的稳定性分析[J]. 力学季刊, 2010,31(1): 64-70.(XIAO Shi-fu, XU Mao. On stability of viscoelastic simply supported beam undergoing overall axially symmetrical rotation[J]. Chinese Quarterly of Mechanics,2010,31(1): 64-70.(in Chinese))
    [22]
    赵婕, 于开平, 学忠. 末端带有刚体的旋转梁运动稳定性分析[J]. 力学学报, 2013,45(4): 606-613.(ZHAO Jie, YU Kai-ping, XUE Zhong. The motion stability analysis of a rotating beam with a rigid body on its end[J]. Chinese Journal of Theoretical and Applied Mechanics,2013,45(4): 606-613.(in Chinese))
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