轻工机械2018，Vol.36Issue(1)：1-3,12,4.DOI:10.3969/j.issn.1005-2895.2018.01.001
机械系统结构动力学方程的李群分析法
Lie Group Analysis Method for Structural Dynamic Equation of Mechanical System
摘要
Abstract
To provide a new approach for the quantitative and qualitative analysis of dynamic characteristics of complex mechanical systems, the modern Lie Group analysis method was introduced into the dynamic analysis of mechanical structures in this paper.First, the conserved quantity form was obtained resulted in limited degree of freedom mechanical vibration system under infinitesimal transformations by matrix decoupling technique;secondly,the Lie point symmetry using continuous mechanical structure of three-dimensional elastodynamic equation allowed the equations of the series of group invariant solutions being constructed.The results show that the mechanical and dynamic phenomena can be obtained by Lie Group analysis.The study can not only get exact solutions of mechanical vibration response,but also provides an effective means of authentication for the numerical calculation.关键词
结构动力学/李群分析法/对称性/守恒量/不变解Key words
structural dynamics/Lie Group analysis/symmetry/conserved quantity/invariant solution分类
通用工业技术引用本文复制引用
郑明亮..机械系统结构动力学方程的李群分析法[J].轻工机械,2018,36(1):1-3,12,4.基金项目
国家自然科学基金项目(11272287) （11272287）
国家自然科学基金项目(11472247). （11472247）
