基于模态综合法的主次结构动力特性分析

发布时间：2018-01-10 20:23

本文关键词：基于模态综合法的主次结构动力特性分析　出处：《武汉理工大学》2015年硕士论文　论文类型：学位论文

【摘要】：模态综合法是解决大型复杂结构动力特性问题的有效方法。它是基于有限元法将复杂结构分为若干子结构,然后对子结构进行动力分析,最后通过模态综合得到组合结构的动力特性。本文首先综述了模态综合法的研究现状,并系统地给出了固定界面模态综合法的基本理论,由于固定界面模态综合法不能有效的缩减界面自由度,所以在对一些大型复杂结构进行模态分析时将会导致计算效率不高。因此本文提出了一种基于模态综合法的主次结构动力特性的研究方法,该方法通过模态综合后的求解矩阵不依赖于主次结构的界面自由度数目,而仅仅取决于主结构和次结构的保留模态数,因此方程阶数得到了有效的缩减,计算效率得到了提高。并注意到了该方法由于忽略了次结构对主结构的影响,所以计算精度不高。然后本文提出了一种修正方法,通过模型缩聚技术,把次结构的缩聚刚度矩阵和质量矩阵分别加到主结构相应的矩阵中,以体现次结构对主结构的影响,并用实例验证了修正后的方法具有较好的精度。本文还提出了模态综合法在有限元分析软件sap2000和数值计算软件MATLAB中的实现路线,并详细介绍了从sap2000中提取模型刚度矩阵和质量矩阵的方法。最后通过对一个包含楼梯的十层框架模型进行研究,将主体框架结构作为主结构,楼梯作为次结构,选取不同的主次结构的保留模态进行计算分析,并将结果与完全有限元方法进行对比。结果显示本文所提方法计算出的组合结构的频率和振型与完全有限元模型所得结果十分接近,并且随着所取主次结构保留模态数的增加,计算结果的精度进一步提高。而且本文中的方法还能有效地计算组合结构特定频率范围内的模态信息,由于仅仅是将目标频率范围内的模态进行综合,所以大大提高了计算效率。
[Abstract]:The modal synthesis method is a effective method to solve the dynamic characteristics of large complex structures. It is based on the finite element method of complex structure is divided into several sub structure and the sub structure dynamic analysis, the dynamic characteristics of composite structures by modal synthesis. This paper reviews the research status of the modal synthesis method, and system are given the basic theory of fixed interface modal synthesis method, the fixed interface mode synthesis method can not effectively reduce the interface degrees of freedom, so will the modal analysis of large complex structure leads to the calculation efficiency is not high. Therefore, this paper proposes a method of dynamic characteristics of primary and secondary structure modal synthesis method based on the interface, the number of degrees of freedom this method does not depend on the primary and secondary structure by solving the matrix synthesis mode, but only depends on the retention of the main structure and secondary structure of the modal number, So the order equation has been effectively reduced, the computational efficiency is improved. And pay attention to this method because of neglecting the influence of structure on the main structure, so the accuracy is not high. Then the paper proposes a correction method, through the model condensation technique, the main structure of the corresponding matrix structure just condensation the stiffness matrix and mass matrix are added, in order to reflect the influence of structure on the main structure, and is used to verify the modified method has good accuracy. This paper also put forward the modal synthesis method in finite element analysis software SAP2000 and numerical calculation software realization route of MATLAB, and introduces the method of rigid model the stiffness matrix and mass matrix extracted from SAP2000. Finally, through the study of a staircase ten floor frame model, the main frame structure as the main structure, the stairs as secondary structure, selecting different Keep the primary and secondary structure of the modal analysis, and the results were compared with the complete finite element method. The results showed the results is very close to the combined structure of the method proposed in this paper to calculate the frequency and vibration type and finite element model of income, and with the increase in the number of primary and secondary structure modal calculation results, further improve the accuracy of the method in this paper. And can effectively calculate the modal information structure specific frequency range, because only the modal frequency range of the target, it greatly improves the computational efficiency.

【学位授予单位】：武汉理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TU311.3

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