A method of modal analysis by proper orthogonal decomposition for large-order systems of arbitrary mass distribution is outlined. The method involves reduced-order modeling of the system mass distribution so that the discretized mass matrix dimension matches the number of sensed quantities, and hence the dimension of the response ensemble and correlation matrix. In this case, the linear interpolation of unsensed displacements is used to perform an effective lumped mass homogenization. The idea is applied to the modal identification of a mass-spring system and an exponential rod.
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Reduced Mass-Weighted Proper Decomposition for Modal Analysis
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Yadalam, VK, & Feeny, BF. "Reduced Mass-Weighted Proper Decomposition for Modal Analysis." Proceedings of the ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Smart Materials, Adaptive Structures and Intelligent Systems, Volume 2. Ellicott City, Maryland, USA. October 28–30, 2008. pp. 477-484. ASME. https://doi.org/10.1115/SMASIS2008-584
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