| 求工程结构最低阶固有频率的一种算法 |
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| 引用本文： | 李惠彬,郑兆昌,等.求工程结构最低阶固有频率的一种算法[J].工程力学,2001,18(4):13-17. |
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| 作者姓名： | 李惠彬 郑兆昌 |
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| 作者单位： | [1]清华大学土木系，北京100084 [2]清华大学力学系，北京100084 |
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| 基金项目： | 国家自然科学基金资助项目（19672033） |
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| 摘 要： | 本文采用子空间迭代法将工程结构高阶动力系统减缩为低阶动力系统，然后用Ｃｏｌｌａｔｚ包含定理的推广求出该结构系统的最低阶固有频率。
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| 关 键 词： | 子空间迭代法 最低阶固有频率 Collatz包含定理 Cholesky三角分解 |
A METHOD FOR CALCULATING THE FUNDAMENTAL NATURAL FREQUENCY OF STRUCTURES |
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| LI Hui-bin,QIN Quan,ZHENG Zhao-chang.A METHOD FOR CALCULATING THE FUNDAMENTAL NATURAL FREQUENCY OF STRUCTURES[J].Engineering Mechanics,2001,18(4):13-17. |
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| Authors: | LI Hui-bin QIN Quan ZHENG Zhao-chang |
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| Abstract: | In this paper, subspace iteration is used to reduce high-order dynamic systems to loworder ones. The Collatz inclusion theorem is extended to Generalized Eigenvalue problems. When the mass matrix or stiffness matrix is positive definite symmetric matrix, the generalized eigenvalue problem is reduced to standard eigenvalue problem by using Cholesky decomposition. The fundamental natural frequency of low-order system is obtained from decomposition of mass matrix and stiffness matrix. To verify the theory, a beam with fixed ends is token as example. The computed result is compared favorably with the exact solution |
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| Keywords: | subspace iteration fundamental natural frequency collatz inclusion theorem Cholesky decomposition |
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