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

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.

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