中间支撑刚度对双跨梁屈曲稳定性的影响

Effect of intermediate support stiffness on buckling stability of a double-span beam

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能足够精确地描述屈曲位形,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。

Here,effects of intermediate elastic support on buckling stability of a double-span beam under axial pressure were studied.By treating the double-span beam as one continuous beam and two beams with an intermediate support,respectively,two beam models were established.By calculating their natural frequencies and critical buckling pressures,the two models were mutually verified,and the variation law of the critical axial force versus stiffness of intermediate support was obtained.Then,the static buckling bifurcation phenomenon of the double-span beam was analyzed by using the continuous beam model,and effects of intermediate constraint stiffness on buckling configuration were discussed.It was shown that when stiffness of intermediate support is less than a critical value,with increase in support stiffness,although the first-order buckling configuration is gradually away from the half periodic sinusoidal configuration of a simply supported buckling beam,it is still stable;higher and higher order modal truncation is needed to obtain the convergent buckling configuration;when stiffness of intermediate support exceeds the critical value,the second-order configuration becomes stable,a single period sine function is enough to accurately describe the beam’s buckling configuration,and stiffness of intermediate support no longer has effects on the critical axial force.This study can provide theoretical guidance for designing beams or pipelines with intermediate supports.