针对局部非线性问题的混合坐标模态综合法

doi:10.7527/S1000-6893.2015.0360

固体力学与飞行器总体设计

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针对局部非线性问题的混合坐标模态综合法

王陶¹, 何欢^1,2, 陈国平^1,2

1. 南京航空航天大学机械结构力学及控制国家重点实验室, 南京 210016;
2. 南京航空航天大学振动工程研究所, 南京 210016

收稿日期:2015-09-09 修回日期:2015-12-28 出版日期:2016-09-15 发布日期:2016-01-19
通讯作者: 何欢男, 博士, 副教授, 硕士生导师。主要研究方向:复杂结构动力学、飞行器回收系统动力学。 Tel.: 025-87138242 E-mail: hehuan@nuaa.edu.cn E-mail:hehuan@nuaa.edu.cn
作者简介:王陶男, 博士。主要研究方向:复杂结构动力学。 Tel.: 025-84892197 E-mail: wangtao813619@163.com;陈国平男, 博士, 教授, 博士生导师。主要研究方向:复杂结构动力学与控制。 Tel.: 025-84892142 E-mail: gpchen@nuaa.edu.cn
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

WANG Tao¹, HE Huan^1,2, CHEN Guoping^1,2

1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2015-09-09 Revised:2015-12-28 Online:2016-09-15 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

摘要/Abstract

摘要：

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。

关键词: 局部非线性, 混合坐标, 自由界面, 模态综合, 协调关系

Abstract:

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.

Key words: localised nonlinearities, hybrid coordinates, free interface, component mode synthesis method, compatibility conditions

中图分类号:

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.

WANG Tao, HE Huan, CHEN Guoping. Component mode synthesis method based on hybrid coordinates for structure with localised nonlinearities[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(9): 2757-2765.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

针对局部非线性问题的混合坐标模态综合法

Component mode synthesis method based on hybrid coordinates for structure with localised nonlinearities

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