绕轴线自转悬臂梁的局部限制失稳分析

Locally Confined Buckling Analysis of Self-Rotating Cantilever Beams

建立了任意位置限位器约束下绕轴线自转悬臂梁的非线性模型.采用Ritz法分析系统的稳定性,获得了限位器无摩擦情形下系统的限制失稳临界值、分岔模式、后屈曲解以及致稳限位器的最佳配置位置.采用有限元法对失稳临界值与致稳限位器的优化位置进行了验证,获得了一致的结果.进一步分析了限位器夹紧力和支撑力摩擦效应对系统稳定性的影响规律,获得了有益的认识.研究表明,在限位器约束下,绕轴线自转悬臂梁存在临界转速,当转速超过临界值时,梁的零挠度平衡位置将发生叉式分岔而失去稳定性;限位器夹紧力摩擦效应将使失稳后的系统在转速回复时出现明显的滞后效应,以比失稳临界值更低的转速回到原平衡位置;绕轴线自转悬臂梁系统致稳限位器的最优配置位置在梁长距固支端的78%左右等.这些成果对提升绕轴线自转悬臂梁的局部限制失稳性能的认识和指导限位器的配置具有实际意义.

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.