Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Engineering Science and Mechanics

Department dc:contributor.department

Engineering Science and Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1997

Author dc:creator

• Just, Frederick A.

Chair dc:contributor.committeechair

• Hendricks, Scott L.

Committee members dc:contributor.committeemember

• Ragab, Saad A.
• Burdisso, Ricardo A.
• Cudney, Harley H.
• Hendricks, Scott L.
• Thangjitham, Surot

• Eigenvalue Problem
• Convex Set
• Damage Detection

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-111297-151222

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/29555