Which are the important modes of a subsystem?
Which are the important modes of a subsystem?
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DOI：
10.1002/nme.935
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发表时间：
2004-03-28
影响因子：
2.9
通讯作者：
Patlashenko, I
中科院分区：
文献类型：
--
作者：
Givoli, D;Barbone, PE;Patlashenko, I
考虑连接到主结构（或主动态系统）的线性行为振动子结构（或更一般地线性动态子系统）。离散化后，子结构由有限的、通常很大的自由度 N-s 表示，因此也由 N-s 特征模态表示。为了减少计算量，通常对子系统应用“模态缩减”，以便仅保留 N-r 个模式总数中的 N-r 个模式，其中 N-r 小于或等于 N-s。接下来的问题就出现了：“应该保留哪些 N-r 模式？”在结构动力学中，传统上保留那些与最低频率相关的模式。在本文中，该问题通过解决适当的优化问题来回答。子系统最重要的模式是那些以特定方式定义的耦合矩阵具有最高范数的模式。这产生了一种简单有效的优化模态缩减算法。 “模态重要性”的新标准从数学和物理角度进行了解释，并通过数值示例进行了证明。版权所有 (C) 2004 John Wiley Sons, Ltd.
A linearly behaving vibrational Substructure (or more generally a linear dynamic subsystem) attached to a main structure (or a main dynamic system) is considered. After discretization, the substructure is represented by a finite, typically large, number of degrees of freedom, N-s and hence also by N-s eigenmodes. In order to reduce the computational effort, it is common to apply 'modal reduction' to the subsystem such that only N-r modes out of the total number of N-r modes are retained, where N-r less than or equal to N-s. The following question then arises: 'Which N-r modes Should be retained?' In structural dynamics, it is traditional to retain those modes associated with the lowest frequencies. In this paper, the question is answered by solving an appropriate optimization problem. The most important modes of the subsystem are shown to be those whose coupling matrices, which are defined in a particular way, have the hi-hest norm. This leads to a simple and effective algorithm for optimal modal reduction. The new criterion for 'modal importance' is explained both mathematically and physically, and is demonstrated by numerical examples. Copyright (C) 2004 John Wiley Sons, Ltd.