刘福顺, 郭鹏, 王超, 董莎莎. 一种模态振型的直接扩阶方法[J]. 工程力学, 2012, 29(8): 28-32. DOI: 10.6052/j.issn.1000-4750.2010.11.0834
引用本文: 刘福顺, 郭鹏, 王超, 董莎莎. 一种模态振型的直接扩阶方法[J]. 工程力学, 2012, 29(8): 28-32. DOI: 10.6052/j.issn.1000-4750.2010.11.0834
LIU Fu-shun, GUO Peng, WANG Chao, DONG Sha-sha. A DIRECT MODE SHAPE EXPANSION METHOD[J]. Engineering Mechanics, 2012, 29(8): 28-32. DOI: 10.6052/j.issn.1000-4750.2010.11.0834
Citation: LIU Fu-shun, GUO Peng, WANG Chao, DONG Sha-sha. A DIRECT MODE SHAPE EXPANSION METHOD[J]. Engineering Mechanics, 2012, 29(8): 28-32. DOI: 10.6052/j.issn.1000-4750.2010.11.0834

一种模态振型的直接扩阶方法

A DIRECT MODE SHAPE EXPANSION METHOD

  • 摘要: 传统的模型缩阶及模态扩阶方法是以计算传递矩阵为手段.该文提出一种实测模态振型空间不完备问题的直接处理方法,即未测试自由度振型值的直接估计方法.通过引入一复合向量,该向量由对应于主自由度的实测振型值与对应于从自由度的待估算值组成.依靠实测模态及有限元模型信息对复合向量中未测试自由度的振型值进行重新估算,进而获得空间完备的模态振型.该文采用5 自由度的弹簧-质量体系验证方法的正确性;借助平面框架结构探讨新方法较传统方法在低阶模态振型估算精度上的优势.数值结果表明:所提出方法不需质量归一化条件以及实测模态与有限元振型的比例条件;同时,该方法较传统方法在低阶模态振型扩阶上具有更好的精度,并允许有限元模型具有一定的模型误差.

     

    Abstract: Traditional methods dealing with spatial incompleteness is by employing transformation matrix for model reduction and modal expansion. This article presents a different mode shape expansion method without obtaining transformation matrix, i.e., a direct mode shape expansion method. A hybrid vector is employed, which is constructed by values corresponding to master degrees of freedom (DOF) and values corresponding to slave DOFs. Spatial complete mode shape is estimated by modifying the above values at slave DOFs based on information such as measured spatial incomplete mode shape and stiffness and mass matrices from the analytical model. A five DOFs mass-spring system is used to examine the accuracy of the proposed method; and a planar frame structure is used to identify the performance for lower order mode shapes estimation. Numerical results show that: 1) Mass normalization and scaling for mode shapes are not needed in the proposed method; and 2) The proposed method outperforms traditional expansion method for lower order mode shape expansion, and a certain modeling errors are permitted in finite element model of the test structure.

     

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