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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