针对局部非线性问题的混合坐标模态综合法
收稿日期: 2015-09-09
修回日期: 2015-12-28
网络出版日期: 2016-01-19
基金资助
国家自然科学基金（11472132）；中央高校基本科研业务费专项资金（NS2014002）；江苏高校优势学科建设工程
Component mode synthesis method based on hybrid coordinates for structure with localised nonlinearities
Received date: 2015-09-09
Revised date: 2015-12-28
Online published: 2016-01-19
Supported by
National Natural Science Foundation of China (11472132); the Fundamental Research Funds for Central Universities (NS2014002); Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions
非线性动力系统模型的计算效率问题是结构动力学领域中的重要研究课题。提出了一种针对局部非线性问题的混合坐标自由界面子结构模态综合方法。根据局部非线性系统的特点，将结构按照线性部分与非线性部分进行分割。线性部分子结构可以通过模态坐标转换到模态空间。在对线性部分进行减缩的过程中考虑了剩余柔度的影响，并通过构造一组与低阶模态关于系统矩阵加权正交的向量组，解决了子结构含有刚体模态时剩余柔度矩阵无法计算的问题。非线性部分子结构则保留原有的物理坐标。通过界面协调关系，采用自由界面方法得到系统混合坐标综合方程。最后，通过数值算例验证了所提出方法的有效性。
王陶 , 何欢 , 陈国平 . 针对局部非线性问题的混合坐标模态综合法[J]. 航空学报, 2016 , 37(9) : 2757 -2765 . DOI: 10.7527/S1000-6893.2015.0360
The calculation efficiency of nonlinear dynamic system has become increasingly important in the structural dynamics field. A hybrid coordinates component mode synthesis method is proposed in this paper for the structure with localised nonlinearities. According to its feature, generally, the system is divided into the linear component and nonlinear component. The equations of the linear component can be transformed into the modal coordinates by its linear vibration modes. In order to improve the accuracy, the residual flexibility attachment matrix of the system is introduced. And by constructing the weighted-orthogonal vector sets which have weighted-orthogonal relationship with the lower retained modes, the residual flexibility attachment matrix is obtained without using inverse of the stiffness matrix. The equations of the nonlinear component are kept as their original form. The synthesis equations which are expressed by hybrid coordinates are derived in terms of compatibility conditions at the interface. Finally, applications of the proposed methods to the numerical examples demonstrate that the present method is computationally effective.
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