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

摘要

Abstract: Shannon's sampling theorem is used here for the firsttime to reconstruct the mode shapes, resulting fromequidistantly spaced sampling points obtained in thefield, associated with building structures. Thefeasibility of reconstructing mode shapes of astructural system using a minimum number of sensors isinvestigated. To evaluate the feasibility of themethod, the first three mode shapes of a simplysupported beam and a mode shape represented by aparabolic equation are reconstructed. We find that theerror between the true mode shapes and thereconstructed mode shapes reduces significantly as thenumber of the repeats of sampling points increases. Thecomparisons between exact and reconstructed mode shapesare presented, in addition to values for the modalassurance criteria (MAC) for the exact andreconstructed modes. The practicality of using thesereconstructed mode shapes obtained via Shannon'ssampling theorem is demonstrated using a recentlydeveloped nondestructive damage localization algorithm.The results show that the reconstructed mode shapes,generated using a minimum number of sensors, can indeedbe used to localize damage. !7