多自由度参激系统稳定性分析的数值解法  

Numerical method for stability analysis of multiple-degree-of-freedom parametric dynamic systems

作　　者：徐梅鹏 李凌峰 任双兴 侯磊[1] 陈予恕[1] XU Mei-peng;LI Ling-feng;REN Shuang-xing;HOU Lei;CHEN Yu-shu(School of Astronautics,Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]哈尔滨工业大学航天学院,哈尔滨150001

出　　处：《计算力学学报》2020年第1期48-52,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11602070);国家重点基础研究发展计划(2015CB057400);中国博士后科学基金(2018T110282,2016M590277);山东省自然科学基金(ZR2016AP06,ZR2018QA005,ZR2018BA021);黑龙江省博士后资助经费(LBH-Z16067)资助项目.

摘　　要：现有参激系统的动力稳定性问题研究主要集中在主不稳定区域上。为获得组合不稳定区域,基于Floquet方法,采用Bolotin方法在不同周期数下设解形式,结合特征值分析法得到确定多自由度参激系统动力不稳定区域的数值解法。对一个两自由度受周期轴向力的旋转轴系算例的稳定性分析,发现通过增加设解近似项数可获得高阶不稳定区域,且各阶不稳定区域边界随近似次数的增加逐渐趋于稳定,此外,增大阻尼可使各不稳定区域边界变得更加平滑。本文方法可用于一般多自由度周期参激阻尼系统,是一种简明易操作的直接数值解法。The study on dynamic stability of a parametric excitation system mainly focuses on the main unstable region.In order to obtain more results of the combined unstable region,the solution form of Bolotin method under different period numbers was applied with the Floquet method.Combined with the eigen value analysis method,the direct numerical solution method for determining the dynamic unstable region of the multi-dof parametric system is obtained.According to the stability analysis of a two-degreeof-freedom rotating shafting with periodic axial force,the high order unstable region is obtained with the increase of approximate terms of solution,and the boundary of each unstable region tends to be stable with the increase of approximate terms.It is found that the damping makes the boundary of each unstable region“smooth”.The method can be applied for general multi-dof periodic parametric damped system and produces a simple and direct numerical solution.

关 键 词：参激系统 动力稳定性 Bolotin方法 Floquet方法 特征值分析法 

分 类 号：V231[航空宇航科学与技术—航空宇航推进理论与工程] O347.2[理学—固体力学]