中间支撑刚度对双跨梁屈曲稳定性的影响

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摘要研究了中间弹性支撑对受轴向压力的双跨梁屈曲稳定性的影响。分别采用整体以及分段方式建立了带中间弹性支撑的双跨梁模型，通过计算固有频率以及临界屈曲压力，相互验证了两种模型，并得到临界轴力随中间支撑刚度的变化规律。在此基础上，用整体梁模型分析双跨梁的静力学屈曲分岔现象，着重讨论了中间约束刚度对屈曲位形的影响。研究发现，在中间支撑刚度小于一个临界值时，随着支撑刚度的增加，虽然一阶屈曲位形逐渐远离简支屈曲梁的半周期正弦位形，但依然是稳定的；只是需要越来越高阶的截断，才能得到收敛的屈曲位形。而当中间支撑刚度超过临界值后，二阶位形变得稳定；仅采用单周期的正弦函数就足够精确描述屈曲位形，并且中间支撑刚度对临界轴力不再产生影响。该研究将为带中间支撑的梁或者管道设计提供理论指导。

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	毛晓晔1
	邵志华1
	舒送2
	范鑫2
	3
	丁虎1
	陈立群1

关键词 ：双跨梁, 屈曲, 压杆稳定, 截断

Abstract：The influence of the supporting stiffness at the middle point on the buckling stability of a two-span beam is investigated for the first time. By treating the two-span beam as one continuous beam and two beams separately, two kinds of governing equations are obtained. Based on these two equations, the natural frequencies and the critical buckling axial force changing with the bearing stiffness at the middle point are studied. The results indicate that both of these two equations are corrected as they can verify each other. Consequently, more detailed investigations are carried out via the continuous model as it is more convenient than the two-beams model. The investigation finds that the bearing stiffness plays a key role in the calculation and the stability of the nontrivial configuration. While the stiffness is increasing, higher order truncation of natural modes is needed to deduce a convergent first-order nontrivial configuration. Meanwhile, the configuration will be far from the half-periodic SIN function but always stable under a critical bearing stiffness. After that, the second-order nontrivial configuration will take the stable position of it. Only the second-order natural mode is accurate enough to describe the new nontrivial configuration. The work proposes some analytical suggestions for the design of beams or pipes with bearings at the middle point.

Key words： two-span beam buckling stability truncation

收稿日期: 2021-02-18 出版日期: 2022-06-15

引用本文:

毛晓晔1，邵志华1，舒送2，范鑫2,3，丁虎1，陈立群1. 中间支撑刚度对双跨梁屈曲稳定性的影响[J]. 振动与冲击, 2022, 41(11): 1-9.
MAO Xiaoye1, SHAO Zhihua1, SHU Song2, FAN Xin2,3, DING Hu1, CHEN Liqun1. Effect of intermediate support stiffness on buckling stability of a double-span beam. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(11): 1-9.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I11/1

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