几何缺陷浅拱的动力稳定性分析

研究了几何缺陷对粘弹性铰支浅拱动力稳定性能的影响。从达朗贝尔原理和欧拉-贝努利假定出发推导了粘弹性铰支浅拱在正弦分布突加荷载作用下的动力学控制方程,并采用Galerkin截断法得到了可用龙格-库塔法求解的无量纲化非线性微分方程组。同时引入能有效追踪结构动力后屈曲路径的广义位移控制法,对含几何缺陷浅拱的响应曲线进行几何、材料双重非线性有限元分析。用这两种方法分析了前三阶谐波缺陷对浅拱动力稳定性能的影响,其中动力临界荷载由B-R准则判定。主要结论有:材料粘弹性使浅拱动力临界荷载增大且结构响应曲线与弹性情况差别很大;二阶谐波缺陷影响显著,它使动力临界荷载明显下降且使得浅拱粘弹性动力临界荷载可能低于弹性动力临界荷载。

The dynamic stability analysis of shallow arches with geometrical imperfections

This paper is concerned with the effects of geometrical imperfections on the dynamic stability of viscoelastic hinged shallow arches.The dynamic equation of shallow arch subjected to sinusoidal impulsive load is derived from the d'Alembert principle and the Euler-Bernoulli assumption.Then with the application of the Galerkin method the nondimensional nonlinear differential equations,which can be solved by the Rungle-Kulta method,are determined.On the other hand the general displacement control method,which can effectively trace the dynamic post-buckling path of structure,is introduced to obtain the response curve of shallow arch with geometrical imperfection in the geometrical and material finite element analysis.These two methods are used to investigate the effects of the first three harmonic geometrical imperfections on the dynamic stabilities of shallow arches,where the critical loads are both determined by the B-R criterion.The main results are firstly that the dynamic critical load of shallow arch is larger when the material is viscoelastic and the differences in the structural response curves are great between viscoelastic and elastic shallow arch,and secondly that the second-order harmonic geometrical imperfection decreases the dynamic critical load remarkably,furthermore the dynamic critical load of viscoelastic shallow arch may be smaller than that of elastic shallow arch.