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基于群论的预应力结构广义特征值分析
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(东南大学混凝土及预应力混凝土结构教育部重点实验室 南京 210096)

作者简介:

陈耀

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中图分类号:

TU378

基金项目:

国家自然科学基金项目(51278116) 东南大学优秀博士学位论文基金项目(YBJJ1025) 江苏高校优势学科建设工程资助项目


Generalized eigenvalue analysis of prestressed structures based on group theory
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(Key Laboratory of Concrete and Prestressed Concrete Structures, Ministry of Education, Southeast University, Nanjing 210096, China)

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    摘要:

    由于常规自振分析方法未能充分利用结构的固有对称性,当结构自由度增加时,计算消耗显著提升。本文基于群论方法,提出一种分析对称型预应力结构动力特性的高效方法。首先,结合一致质量矩阵及切线刚度矩阵建立了预应力结构的广义特征方程,并考虑初始预应力对结构的影响,以求解结构的自振频率及振型。随后,建立对称坐标系,将刚度矩阵及质量矩阵分解为一系列分块对角化矩阵。由于各分块子矩阵相互独立,广义特征值问题的求解难度显著降低,从而能高效求解结构的自振频率及相应振型。数值算例阐明了所提出方法的基本计算过程及显著优势。与有限元结果及常规方法所得结果比较后可知,基于群论的对称方法准确、高效。

    Abstract:

    Because the conventional method of natural vibration analysis fails to make full use of the inherent symmetry of the structure, the calculation cost increases significantly when the degree of freedom of the structure increases. Based on group theory, an efficient method for analyzing the dynamic characteristics of symmetrical prestressed structures is presented in this paper. Firstly, the generalized characteristic equation of the prestressed structure is established by combining the uniform mass matrix and tangential stiffness matrix, and the influence of the initial prestress on the structure is considered to solve the natural vibration frequency and mode of the structure. Then, a symmetric coordinate system is established to decompose the stiffness matrix and mass matrix into a series of partitioned diagonalized matrices. Because each submatrix is independent of each other, the difficulty of solving the generalized eigenvalue problem is significantly reduced, and the natural frequency and corresponding mode of the structure can be efficiently solved. Numerical examples illustrate the basic calculation process and significant advantages of the proposed method. Compared with the results of finite element method and conventional method, the symmetry method based on group theory is accurate and efficient.

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引用本文

Yao Chen, Jian Feng Generalized eigenvalue analysis of prestressed structures based on group theory. Prestress Technology 2015,19(05):3-25. 10.59238/j. pt.2015.05.001

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  • 在线发布日期: 2023-08-06
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