Development of a Technique to Locate and Quantify a Crack in a Beam Based on Modal Parameters

[+] Author and Article Information
M. Karthikeyan

Department of Mechanical Engineering, Indian Institute of Technology, Guwahati 781039, Indiakarthikeyan@iitg.ernet.in

R. Tiwari1

Department of Mechanical Engineering, Indian Institute of Technology, Guwahati 781039, Indiartiwari@iitg.ernet.in

S. Talukdar

Department of Civil Engineering, Indian Institute of Technology, Guwahati 781039, India


Corresponding author.

J. Vib. Acoust 129(3), 390-395 (Oct 12, 2006) (6 pages) doi:10.1115/1.2424981 History: Received December 29, 2005; Revised October 12, 2006

A model-based algorithm has been developed, in order to locate and quantify the size of a crack, based on free vibration measurements of a cracked beam. Measured natural frequencies (at least two) and corresponding mode shapes of the cracked beam are used in the identification algorithm. The Euler–Bernoulli beam theory is used to model the beam. The crack of the beam is modeled through standard five crack flexibility coefficients, by considering bending effects only. Damping is assumed to be Rayleigh’s damping. The finite element method is used in the simulation of the cracked beam. The present algorithm is iterative in nature and the iterations are carried out until the estimated and assumed crack depth ratios (as well as its location) become close up to the desired accuracy. The applicability of the algorithm has been tested through numerical examples and is found to be adequate even in the presence of the measurement noise in modes shapes and measurement errors in natural frequencies.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A cracked beam element in a general loading

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Figure 2

The flow chart for the proposed crack localization and sizing algorithm

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Figure 3

(a) The first mode shape; and (b) second mode shape of the cracked and uncracked beam

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Figure 4

Variation of natural frequency ratios versus crack positions for different crack depth ratios

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Figure 5

A procedure for the location of the crack using the experimental and computational natural frequencies



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