Sensitivity of Uniform Load Surface Curvature for Damage Identification in Plate Structures

Abstract

In this paper a new sensitivity-based method of using measured modal parameters to locate and quantify damage is developed for plate-like structures. With the measured incomplete modal data for only the few lower modes in both the intact and damaged states, the two-dimensional distributed curvatures of uniform load surface (ULS) over the plate are approximated using the Chebyshev polynomials. Instead of directly comparing the curvatures before and after damage, like many existing damage localization methods using curvature techniques, e.g., mode shape curvature and flexibility curvature, the proposed method analytically studies the sensitivity of the ULS curvature with respect to the element-by-element stiffness parameters. The changes in the elemental stiffness parameters due to damage give the location and magnitude of the damaged plate elements. Based on the first-order Taylor series approximation, the inverse problem is modeled as a linear equation system and solved iteratively using truncated SVD technique. Numerical simulations are performed to verify the effectiveness of the proposed method with different support conditions, measurement noise, and sensor sparsity.