Effect of intermediate support stiffness on buckling stability of a double-span beam
MAO Xiaoye1, SHAO Zhihua1, SHU Song2, FAN Xin2,3, DING Hu1, CHEN Liqun1
Author information+
1.Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China;
2.The 5720th Factory of PLA, Wuhu 241007, China;
3.Department of Precision Machinery and Precision Instruments, University of Science and Technology of China, Hefei 230026, China
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.
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[J]. Journal of Vibration and Shock, 2022, 41(11): 1-9
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