Crack detection on a cantilever beam using the nearest approximation method

Frederick A. Just; Scott L. Hendricks

doi:10.1117/12.207723

20 April 1995 Crack detection on a cantilever beam using the nearest approximation method

Frederick A. Just, Scott L. Hendricks

Proceedings Volume 2446, Smart Structures and Materials 1995: Smart Systems for Bridges, Structures, and Highways; (1995) https://doi.org/10.1117/12.207723
Event: Smart Structures and Materials '95, 1995, San Diego, CA, United States

Abstract

This paper deals with determination of damage location and magnitude evaluation by measuring the natural frequencies of a structure. A uniform transverse crack, located on a steel cantilever prismatic beam of rectangular cross section, is used as the model for damage. The crack on the beam is assumed to be open during the transverse vibration of the structure, thus the effect of closing and opening of the crack is ignored in the analysis. Euler-Bernoulli beam behavior is modeled and the damage effect (crack location and depth) is modeled as a torsional spring. The equations of motion of the beam with the crack are developed from Hamilton's principle. The natural frequencies for various crack depths and locations are calculated to establish a collection of failure sets. The response from an actual beam is then compared to the collection of failure sets. The failure set that most nearly approximates the actual response is used to identify the crack location and depth. This method is confirmed with the experimental vibration of a steel cantilever beam. This beam has a single damage location and the damage (crack depth) is increased by fatigue loading. The method is valid as long as the response of any of the failure sets do not overlap into the response of other failure sets. The accuracy of this procedure depends upon the type of failure sets used, (mathematical model to predict response) and the response of the system to the actual failure. The advantages and disadvantages of the method are discussed.

Citation Download Citation

Frederick A. Just and Scott L. Hendricks "Crack detection on a cantilever beam using the nearest approximation method", Proc. SPIE 2446, Smart Structures and Materials 1995: Smart Systems for Bridges, Structures, and Highways, (20 April 1995); https://doi.org/10.1117/12.207723

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KEYWORDS

Mathematical modeling

Failure analysis

Motion models

Inspection

Damage detection

Mechanics

Differential equations

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