Reconstruction of mode shapes using Shannon's sampling theorem and its application to the nondestructive damage localization algorithm

Sooyong Park; Norris Stubbs

doi:10.1117/12.207737

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20 April 1995 Reconstruction of mode shapes using Shannon's sampling theorem and its application to the nondestructive damage localization algorithm

Sooyong Park, Norris Stubbs

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Proceedings Volume 2446, Smart Structures and Materials 1995: Smart Systems for Bridges, Structures, and Highways; (1995) https://doi.org/10.1117/12.207737
Event: Smart Structures and Materials '95, 1995, San Diego, CA, United States

Abstract

Shannon's sampling theorem is used here for the first time to reconstruct the mode shapes, resulting from equidistantly spaced sampling points obtained in the field, associated with building structures. The feasibility of reconstructing mode shapes of a structural system using a minimum number of sensors is investigated. To evaluate the feasibility of the method, the first three mode shapes of a simply supported beam and a mode shape represented by a parabolic equation are reconstructed. We find that the error between the true mode shapes and the reconstructed mode shapes reduces significantly as the number of the repeats of sampling points increases. The comparisons between exact and reconstructed mode shapes are presented, in addition to values for the modal assurance criteria (MAC) for the exact and reconstructed modes. The practicality of using these reconstructed mode shapes obtained via Shannon's sampling theorem is demonstrated using a recently developed nondestructive damage localization algorithm. The results show that the reconstructed mode shapes, generated using a minimum number of sensors, can indeed be used to localize damage.

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Sooyong Park and Norris Stubbs "Reconstruction of mode shapes using Shannon's sampling theorem and its application to the nondestructive damage localization algorithm", Proc. SPIE 2446, Smart Structures and Materials 1995: Smart Systems for Bridges, Structures, and Highways, (20 April 1995); https://doi.org/10.1117/12.207737

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