Keywords: damage detection, damage index, curvature of mode shape, modal flexibility, singular value decomposition, plates.

The problem addressed in this study is to find changes in the stiffness of a structure given measured changes in the modal parameters. A newly developed vibration-based nondestructive damage evaluation technique for a plate-like structure is introduced. A few of lower measured mode shapes before and after a small damage event are required to evaluate damage. The proposed method is capable of detecting, locating, and sizing structural damage in a plate-like structure simultaneously.

The proposed method basically shares with the same idea with the damage index (DI) method by Stubbs et al. [1] and the mode shape curvature (MSC) method by Pandey et al. [2], and possibly extends the efficiency, accuracy, and reliability of those methods by resolving the mode selection problem and the singularity problem near inflection points of mode shape. One strategy taken in this study for the mode selection problem might exploit the concept of modal flexibility because modal flexibility is a rational way to combine the measured modes. In order to resolve the singularity problem, this study solves a governing equation of a damage mechanism that represents a rigorous structural relationship between changes in stiffness and changes in modal flexibility based on the fundamentals of structural mechanics.

Introducing the small damage assumption, the flexural damage index equations (FDIE) for a plate-like structure have been derived from the two-dimensional slop-deflection equations. Next, an efficient solution procedure has been introduced to solve a set of the FDIEs of a structure. Finally, the performance of the proposed method has been numerically evaluated for a simply supported plate structure, and the results are compared with those of the DI and MSC method.

This study confirms that there is a strong linear relationship between the curvature of modal flexibility and flexural damage in the selected class of structures. It is concluded that the proposed method provides a way to avoid the singularity problem and mode selection problem of the MSC and DI method.

1

N. Stubbs, J.T. Kim, K. Topole, "An Efficient and Robust Algorithm for Damage Localization in Offshore Platforms", ASCE 10th Structures Congress '92, San Antonio, Texas, 543-546, 1992.

2

A.K. Pandey, M. Biswas, M.M. Samman, "Damage Detection from Changes in Curvature Mode Shapes", Journal of Sound and Vibration, 145(2), 321-332, 1991. doi:10.1016/0022-460X(91)90595-B

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