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A local correspondence principle for mode shapes in structural dynamics

机译:结构动力学中模式形状的局部对应原理

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It is well known that experimentally obtained mode shapes can be smoothed by using a linear combination of mode shapes from a finite element (FE) model. This is known from the theory of structural modification (SM) and from the system equivalent reduction expansion process (SEREP). Using this approach the set of FE mode shapes to be included in the smoothing must be chosen a priori and the quality of the smoothing and a subsequent mode shape expansion depend significantly on this choice. The present paper provides a solution to the problem of choosing which mode shapes are the most important for the smoothing and how many of the mode shapes should be included in order to obtain an optimal solution. It is shown based on the classical sensitivity theory that for each experimental mode shape, a mode shape cluster can be defined for the mode shapes of the FE model that defines an optimal choice for the smoothing set. The sequence of FE mode shapes to be included in this mode shape cluster is prescribed by a simple principle denoted the principle of local correspondence (LC) the name referring to the fact that an experimentally obtained mode shape should not be considered as corresponding to a single FE mode shape, but rather as corresponding to the mentioned mode shape cluster. A test case for a steel plate is considered where the experimentally obtained mode shapes are smoothed using SEREP (using a fixed set of mode shapes) and using the LC principle, and it is shown that the LC principle secures a high quality of the smoothing whereas the SEREP provides results that are strongly dependent upon the actual choice of the included FE mode shapes and on the degrees of freedom included in the fitting set.
机译:众所周知,可以通过使用有限元(FE)模型中模态形状的线性组合来平滑实验获得的模态形状。从结构修改理论(SM)和系统等效折减展开过程(SEREP)可以知道这一点。使用这种方法,必须先选择要包括在平滑中的FE模式形状集,并且平滑的质量和随后的模式形状扩展很大程度上取决于此选择。本文为选择哪种模式形状对平滑最重要以及应该包含多少个模式形状以获得最佳解决方案的问题提供了解决方案。根据经典灵敏度理论表明,对于每个实验模式形状,可以为FE模型的模式形状定义一个模式形状簇,该模型定义了平滑集的最佳选择。包含在此模式形状簇中的FE模式形状的顺序由表示为局部对应性原理(LC)的简单原理规定,该名称指的是以下事实:实验获得的模式形状不应视为对应于单个FE模式形状,而是对应于提到的模式形状簇。考虑钢板的测试案例,其中使用SEREP(使用一组固定的模态形状)并使用LC原理对实验获得的模态形状进行平滑处理,结果表明LC原理可确保高质量的平滑处理,而SEREP提供的结果很大程度上取决于所包含的有限元模式形状的实际选择以及拟合集中所包含的自由度。

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