旋转简支梁的局部限制失稳分析

发布时间：2018-03-07 18:08

本文选题：广义Hamilton变分原理　切入点：限制失稳　出处：《应用力学学报》2016年05期 　论文类型：期刊论文

【摘要】：应用广义Hamilton变分原理,建立了任意位置限位器约束下绕轴线自转简支梁的非线性模型。取简支梁前两阶模态为Ritz基分析系统的稳定性,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。扩充Ritz基对失稳临界值和限位器最佳配置位置的收敛性进行了验证;进一步分析了限位器夹紧力摩擦效应对系统稳定性的影响规律。研究表明:在限位器约束下,绕轴线自转简支梁存在临界转速,当转速超过临界转速时,梁的挠度和轴向位移分别发生叉式分岔和跨临界分岔而失去稳定性;限位器夹紧力摩擦效应将提升失稳临界值,使失稳后的系统在转速返回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;绕轴线自转简支梁系统致稳限位器的最佳配置位置在梁长的中间。这些结果对提升绕轴线自转简支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]:Based on the generalized Hamilton variational principle, a nonlinear model of a simply supported beam with rotation around an axis is established under the constraint of an arbitrary position limiter. The first two modes of the simply supported beam are taken as the stability of the Ritz basis analysis system. The limit instability critical value, bifurcation mode, post-buckling solution and the optimal configuration position of the stabilizer are obtained under the condition of no friction. The convergence of the instability critical value and the optimal configuration position of the limiter is verified by the extended Ritz basis. The influence of clamping force friction effect on the stability of the system is further analyzed. The results show that there is a critical speed of the simply supported beam rotating around the axis under the constraint of the limiter, and when the rotational speed exceeds the critical speed, The deflection and axial displacement of the beam are forked bifurcation and transcritical bifurcation, respectively, and the friction effect of clamping force of the limiter will increase the critical value of instability and make the system after the instability appear obvious hysteresis effect when the rotational speed returns. Return to the original equilibrium position at a speed lower than the critical value of instability; The optimal position of the stability limiter is in the middle of the beam length. These results are of practical significance to the understanding of the local limited instability performance of the rotating simply supported beam around the axis and the configuration of the locator.
【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) 中物院发展基金(2015B0201024) 中国工程物理研究院重点学科项目“计算固体力学”资助
【分类号】：O317

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