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Research Papers

Nonlinear Dynamics and Damage Assessment of a Cantilever Beam With Breathing Edge Crack

[+] Author and Article Information
Animesh Chatterjee

Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur 440011, Indiaachatterjee@mec.vnit.ac.in

J. Vib. Acoust 133(5), 051004 (Jul 26, 2011) (6 pages) doi:10.1115/1.4003934 History: Received February 04, 2010; Revised January 20, 2011; Published July 26, 2011; Online July 26, 2011

Failures in structures and machine elements can be prevented through early detection of fatigue cracks using various nondestructive testing methods. Vibration testing forms one of the most effective and recent one among these methods. There are mainly two approaches to crack detection through vibration testing: open crack model and breathing crack model. The present study is based on breathing crack model, in which the nonlinear vibration response under harmonic excitation is formulated through Volterra series and higher order frequency response functions. Bilinear stiffness characteristic of a cracked cantilever beam is approximated by a truncated polynomial series and response amplitudes of various harmonics are investigated for both qualitative and quantitative characterization. A new procedure is suggested whereby the presence of a breathing crack in a structure can be first identified and then the severity of the damage can be estimated through harmonic probing.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) A cantilever beam with an edge crack. (b) Finite element discretization of the cracked beam

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Figure 2

A spring-mass damper model of bilinear oscillator

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Figure 3

Bilinear restoring force for α=0.9 and 0.8

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Figure 4

Curve-fitting of bilinear restoring force (α=0.9) through polynomial approximation

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Figure 5

Response harmonic amplitudes for α=0.9

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Figure 6

(a) Response spectrum for bilinear oscillator with excitation frequency, r=0.4. (b) Variation of second harmonic amplitude with excitation level for bilinear and square form nonlinearity.

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Figure 7

(a) Second harmonic amplitudes at α=0.95, 0.9, and 0.8. (b) Harmonic amplitude ratio X(2ω)/X(ω) for a growing crack.

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