Representation of Damping Matrix
Representation of Damping Matrix
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DOI：
10.1061/(asce)0733-9399(1991)117:5(1005
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发表时间：
1991-05
期刊：
影响因子：
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通讯作者：
Z. Liang;G. C. Lee
中科院分区：
文献类型：
--
作者：
Z. Liang;G. C. Lee
本文讨论了用质量矩阵和刚度矩阵表示阻尼矩阵的方法。提出了一种既可以表示瑞利阻尼，也可以表示一般非比例阻尼的关系式。这种关系在数学上基于矩阵表示定理，在某些情况下（可以很容易地检验），矩阵C可以被两个给定矩阵M和K的多项式精确地表示。在工程应用中，在最小二乘法或级数解的意义上，给定矩阵M和K的多项式的前几项被证明足以精确地表示阻尼矩阵。试图解释所提出的阻尼矩阵的一些参数的物理意义。数值算例表明，该方法适用于结构动力学中的非比例阻尼问题，简单、准确。该方法也可应用于系统…
This paper deals with the representation of the damping matrix in terms of mass and stiffness matrices. A relationship is proposed that can represent not only Rayleigh damping, but also the general nonproportional damping. This proposed relationship is mathematically based on a theorem of matrix representation that, under certain circumstance (which can be easily checked), a matrix C can be represented accurately by a polynomial of two given matrices M and K. In engineering applications, in the sense of least‐squares approach or series solutions, the first few terms of the polynomial of the given matrices M and K are shown to be sufficiently accurate to represent the damping matrix. An attempt is made to interpret the physical meaning of some of the parameters of the proposed damping matrix. Numerical examples are given to illustrate the simplicity and accuracy of the proposed method as applied to nonproportional damping problems in structural dynamics. The proposed approach can also be applied in system ...