| 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 |
| 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 |
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| DOI：10.3969/j.issn.1005 2895.2018.01.001 |
| 中文关键词: 结构动力学 李群分析法 对称性 守恒量 不变解 |
| 英文关键词:structural dynamics Lie Group analysis symmetry conserved quantity invariant solution |
| 基金项目:国家自然科学基金项目（11272287）；国家自然科学基金项目（11472247） |
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| 中文摘要: |
| 为给复杂机械系统动力学特性定量和定性分析提供一个强有力的新途径，笔者将现代李群分析方法引入到机械结构动力学中。首先，通过矩阵解耦技术得到有限自由度机械结构振动系统在无限小群变换下导致的守恒量形式；其次，利用机械连续结构体三维弹性动力学方程允许的李点对称构造出方程组的系列群不变解。结果表明借助李群分析可以得到机械系统结构动力学更深层次的力学规律和运动现象。本研究不仅可以得到结构振动响应的精确解，同时也为数值计算提供了有效的验证手段。 |
| 英文摘要: |
| 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. |
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