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Shock and Vibration
Volume 2017 (2017), Article ID 2617534, 11 pages
Research Article

Scaling Mode Shapes in Output-Only Structure by a Mass-Change-Based Method

School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China

Correspondence should be addressed to Hanwen Song

Received 5 February 2017; Accepted 27 March 2017; Published 26 April 2017

Academic Editor: Tai Thai

Copyright © 2017 Liangliang Yu and Hanwen Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A mass-change-based method based on output-only data for the rescaling of mode shapes in operational modal analysis (OMA) is introduced. The mass distribution matrix, which is defined as a diagonal matrix whose diagonal elements represent the ratios among the diagonal elements of the mass matrix, is calculated using the unscaled mode shapes. Based on the theory of null space, the mass distribution vector or mass distribution matrix is obtained. A small mass with calibrated weight is added to a certain location of the structure, and then the mass distribution vector of the modified structure is estimated. The mass matrix is identified according to the difference of the mass distribution vectors between the original and modified structures. Additionally, the universal set of modes is unnecessary when calculating the mass distribution matrix, indicating that modal truncation is allowed in the proposed method. The mass-scaled mode shapes estimated in OMA according to the proposed method are compared with those obtained by experimental modal analysis. A simulation is employed to validate the feasibility of the method. Finally, the method is tested on output-only data from an experiment on a five-storey structure, and the results confirm the effectiveness of the method.