Dynamic condensation of mass and stiffness matrices
- Publication Type:
- Journal Article
- Journal of Sound and Vibration, 1995, 188 (4), pp. 601 - 615
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Details are given of a procedure for condensing the mass and stiffness matrices of a structure for dynamic analysis. The condensed model is based on choosingncnatural frequencies and the corresponding modes of original model. The model is constructed so that (1) it hasncnatural frequencies equal to those of the original model, (2) the modes φifcless than i, j = 1, 2, . . ., ncare the same as those for the master co-ordinates in the corresponding modes of the original and (3) the responses of the condensed system at the co-ordinatesXcdue to forces at these co-ordinates, at one particular chosen frequency, are the same as those of the original system. The natural frequencies, the corresponding modes and the dynamic responses used for the condensation can be obtained from finite element analysis of the original structure. The method has been applied to the modelling of two common structures to examine its applicability. Comparisons between the performance of the condensed models obtained by means of the dynamic condensation method and that of the models obtained by the Guyan method have been conducted. The results of the example show that the condensed models determined by the dynamic condensation method retain the natural frequencies and modal shapes and perform better in describing the dynamic responses of the structures than do the corresponding models obtained by the Guyan method. © 1995 Academic Press. All rights reserved.
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