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Research Papers

An Efficient Method for Crack Identification in Simply Supported Euler–Bernoulli Beams

[+] Author and Article Information
L. Rubio1

Department of Mechanical Engineering, University Carlos III of Madrid, 28911 Madrid, Spainlourdes.rubio@uc3m.es

1

Corresponding author.

J. Vib. Acoust 131(5), 051001 (Sep 09, 2009) (6 pages) doi:10.1115/1.3142876 History: Received September 20, 2007; Revised December 08, 2008; Published September 09, 2009

An effective crack identification procedure has been developed based on the dynamic behavior of a Euler–Bernoulli cracked beam. It is very well known that the presence of a crack in a structure produces a change in its frequency response that can be used to determine the crack properties (position and size) solving what is called an inverse problem. In this work, such an inverse problem has been solved by the use of the classical optimization technique of minimizing the least square criterion applied to the closed-form expression for the frequencies obtained through the perturbation method. The advantage of this method with respect to the ones derived previously is that the knowledge of the material and its properties (Young’s modulus and mass density) is not necessary, not even the behavior of the uncracked element. The methodology has been successfully applied to a simply supported Euler–Bernoulli beam.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Simply supported cracked beam

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Figure 2

Error in crack size estimation versus crack position ratio for different values of crack depth ratio

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Figure 3

Error in crack position estimation versus crack position ratio for different values of crack depth ratio

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Figure 4

Error in the estimations of α, γ, and c for different values of crack depth ratio

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