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Shock and Vibration
Volume 19, Issue 2, Pages 175-186

A Theoretical and Experimental Investigation on Free Vibration Vehavior of a Cantilever Beam with a Breathing Crack

M. Rezaee and H. Fekrmandi

Mechanical Engineering Department, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran

Received 20 March 2010; Revised 6 December 2010

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper the free nonlinear vibration behavior of a cracked cantilever beam is investigated both theoretically and experimentally. For simplicity, the dynamic behavior of a cracked beam vibrating at its first mode is simulated using a simple single degree of freedom lumped parameter system. The time varying stiffness is modeled using a harmonic function. The governing equation of motion is solved by a perturbation method – the method of Multiple Scales.

Results show that the correction term that is added to the main part of the response reflects the effect of breathing crack on the vibration response. Moreover, this part of response consists of the superharmonic components of the spectrum which is due to the system's intrinsic nonlinearity. Using this method an analytical relation is established between the system characteristics and the crack parameters in one hand and the nonlinear characteristics of system response on the other hand. Results have been validated by the experimental tests and a numerical method.