绕轴线自转悬臂梁的局部限制失稳分析
发布时间：2018-08-16 14:53
【摘要】：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.
[Abstract]:A nonlinear model of cantilever beam with axial rotation under arbitrary position limiter constraint is established. The Ritz method is used to analyze the stability of the system. The critical value of the limited instability, bifurcation mode, post-buckling solution and the optimal configuration of the stabilizer are obtained under the condition that the limiter has no friction. The finite element method is used to verify the critical value of instability and the optimal position of the stabilizer, and the results are consistent. Furthermore, the influence of clamping force and supporting force on the stability of the system is analyzed. The results show that the critical rotational speed exists in the cantilever beam around the axis under the constraint of the limiter. When the rotation speed exceeds the critical value, the zero deflection equilibrium position of the beam will have fork bifurcation and lose its stability. The friction effect of clamping force of the limiter will cause obvious hysteresis effect in the speed recovery of the unstable system, and return to the original equilibrium position at the speed lower than the critical value of the instability. The optimal position of the stability limiter of the cantilever system is about 78% of the fixed end of the beam. These results are of practical significance to the understanding of the local limited instability of the cantilever beam around the axis and to the configuration of the limiter.
【作者单位】： 中国工程物理研究院总体工程研究所;
【基金】：国家自然科学基金(11402244)~~
【分类号】：O344.1
，
本文编号：2186315
[Abstract]:A nonlinear model of cantilever beam with axial rotation under arbitrary position limiter constraint is established. The Ritz method is used to analyze the stability of the system. The critical value of the limited instability, bifurcation mode, post-buckling solution and the optimal configuration of the stabilizer are obtained under the condition that the limiter has no friction. The finite element method is used to verify the critical value of instability and the optimal position of the stabilizer, and the results are consistent. Furthermore, the influence of clamping force and supporting force on the stability of the system is analyzed. The results show that the critical rotational speed exists in the cantilever beam around the axis under the constraint of the limiter. When the rotation speed exceeds the critical value, the zero deflection equilibrium position of the beam will have fork bifurcation and lose its stability. The friction effect of clamping force of the limiter will cause obvious hysteresis effect in the speed recovery of the unstable system, and return to the original equilibrium position at the speed lower than the critical value of the instability. The optimal position of the stability limiter of the cantilever system is about 78% of the fixed end of the beam. These results are of practical significance to the understanding of the local limited instability of the cantilever beam around the axis and to the configuration of the limiter.
【作者单位】： 中国工程物理研究院总体工程研究所;
【基金】：国家自然科学基金(11402244)~~
【分类号】：O344.1
，
本文编号：2186315
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