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Shock and Vibration
Volume 2018, Article ID 2579419, 12 pages
Research Article

The Effects of Breathing Behaviour on Crack Growth of a Vibrating Beam

1School of Aeronautic Manufacturing Engineering, Nanchang Hangkong University, Nanchang, Jiangxi 330063, China
2Department of Aerospace Engineering and Mechanics, The University of Alabama, Tuscaloosa, AL 35487, USA

Correspondence should be addressed to Wenguang Liu; nc.ude.uhcn@41gwuil

Received 10 October 2017; Revised 28 January 2018; Accepted 7 February 2018; Published 11 March 2018

Academic Editor: Mahmoud Bayat

Copyright © 2018 Wenguang Liu and Mark E. Barkey. 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.


The effects of breathing behaviour on the dynamic response and crack growth are studied through a cracked cantilever beam. The main goal is to reveal the coupling mechanism of dynamic response and crack growth by employing a plain single-degree-of-freedom (SDOF) lumped system with the breathing crack stiffness and friction damping. The friction damping loss factor is derived by using Coulomb friction model and energy principle. Natural frequency, dynamic stress, dynamic stress intensity factor (DSIF), and crack growth are analyzed by case studies in the end. Results indicate that not only does the stiffness oscillates during crack growth corresponding to the physically open and closed states of the crack, but also stiffness and friction damping oscillate nonlinearly with crack growth. This behaviour induces not only nonlinear dynamic response but also nonlinear crack growth. It provides an approximate description of the nonlinearities introduced by the presence of a breathing crack. Therefore, it can be employed to improve the prediction precision of the crack identification and crack growth life of a cracked cantilever beam.