超前支护立柱动力稳定性与可靠性研究
Advance Support Column Dynamic Stability and Reliability Research
刘明 1肖康飞1
作者信息
- 1. 辽宁石油化工大学环境与安全工程学院,辽宁抚顺 113001
- 折叠
摘要
针对超前支护立柱顶端受轴向载荷作用,建立立柱阶梯柱形结构的动力偏微分方程,经过转化为二阶常微分Mathieu型参数方程,利用Bolotin方法对其动力稳定性进行数值计算.建立立柱结构的安全余量方程,并成功求解动力不稳定区域边界.分别分析活柱与缸筒不同长度比、立柱不同弹性模量以及活柱与缸筒不同直径比等因素对立柱动力稳定性的影响.结果表明:随着活柱与缸筒长度比的增大,立柱稳定性降低;随着立柱弹性模量和活柱与缸筒直径比的增大,立柱稳定性提高.在此基础上,进行立柱结构的非概率可靠性分析,得到立柱结构的非概率可靠度,即立柱结构的非概率可靠度与活柱和缸筒长度比增减性相反,与立柱弹性模量、活柱与缸筒直径比增减性相同.
Abstract
The dynamic partial differential equations of the stepped column structure were established for the top of the overrun support column subjected to axial loads,which were transformed into second-order ordinary differential Mathieu-type parametric equations,thus numerically calculating dynamic stability of the cotumn by Bolotin method.The safety margin equation of column structure is established and the boundaries of the dynamically unstable region were successfully solved.The effects of different length ratio of live column to cylinder,different elastic modulus of column and different diameter ratio of live column to cylinder on the dynamic stability of column were analyzed.The results show that the stability of the column decreases with the increase of the length ratio of live column to cylinder.The stability of the column is improved with the increase of the elastic modulus of the column and the diameter ratio of the live column to the cylinder.On this basis,the non-probabilistic reliability analysis of the column structure is carried out,and the non-probabilistic reliability of the column structure is obtained,that is,the non-probabilistic reliability of the column structure is opposite to the increase or decrease of the ratio of the length of the column and the cylinder,and same to the increase or decrease of the ratio of the column elastic modulus and the ratio of the live column and the cylinder diameter.
关键词
超前支护/动力稳定性/Mathieu方程/立柱/非概率可靠性Key words
advance support/dynamic stability/mathieu equation/column/non-probabilistic reliability引用本文复制引用
基金项目
抚顺市抚顺英才计划青年拔尖人才资助项目(FSYC202107004)
出版年
2024
NETL
NSTL
万方数据