Structural damage assessment using a generalized minimum rank perturbation theory
Abstract
Recently, the authors proposed computationally attractive algorithms to determine the location and extent of structural damage for undamped structures assuming damage results in a localized change in stiffness properties. The algorithms make use of a finite element model and a subset of measured eigenvalues and eigenvectors. The developed theories approach the damage location and extent problem in a decoupled fashion. First, a theory is developed to determine the location of structural damage. With location determined, a damage extent theory is then developed. The damage extent algorithm is a minimum rank perturbation, which is consistent with the effects of many classes of structural damage on a finite element model. In this work, the concept of the Minimum Rank Perturbation Theory (MRPT) is adopted to determine the damage extent on the inertial properties of an undamped structure. In addition, the MRPT is extended to the case of proportionally damped structures. For proportionally damped structures, the MRPT is used to find the damage extent in any two of the three structural property matrices (mass, damping or stiffness). Finally, illustrative case studies using both numerical and actual experimental data are presented.
 Publication:

AIAA/ASME/ASCE/AHS/ASC 34th Structures, Structural Dynamics, and Materials Conference
 Pub Date:
 April 1993
 Bibcode:
 1993ssdm.conf.1529K
 Keywords:

 Damage Assessment;
 Finite Element Method;
 Large Space Structures;
 Perturbation Theory;
 Stiffness Matrix;
 Algorithms;
 Frequency Response;
 Structural Vibration;
 Structural Weight;
 Structural Mechanics