Communications Project

Document Type:Dissertation
Name:Frederick A. Just
Title:Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem
Degree:Doctor of Philosophy
Department:Enginering Science and Mechanics
Committee Chair: Dr. Scott L. Hendricks
Committee Members:Dr. Scott L. Hendricks
Dr. Harley H. Cudney
Dr. Surot Thangjitham
Dr. Ricardo A. Burdisso
Dr. Saad A. Ragab
Keywords:Damage Detection, Convex Set, Eigenvalue Problem
Date of defense:December 9, 1997
Availability:Release the entire work immediately worldwide.


A method that can be used to detect damage in structures is developed. This method is based on the convexity of the geometric interpretation of the eigenvalue problem for undamped positive definite systems. The damage detection scheme establishes various damage scenarios which are used as failure sets. These scenarios are then compared to the structure's actual response by measuring the natural frequencies of the structure and using a Euclideian norm. Mathematical models were developed for application of the method on a cantilever beam. Damage occurring at a single location or in multiple locations was estalished and studied. Experimental verification was performed on serval prismatic beams in which the method provided adequate results. The exact location and extent of damage for several cases was predicted. When the method failed the prediction was very close to the actual condition in the structure. This method is easy to use and does not require a rigorous amount of instrumentation for obtaining the experimental data required in the detection scheme.

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