TY - JOUR
T1 - Nonlinear pseudo-force in a breathing crack to generate harmonics
AU - Xu, Wei
AU - Su, Zhongqing
AU - Radzieński, Maciej
AU - Cao, Maosen
AU - Ostachowicz, Wiesław
N1 - Funding Information:
This work is supported by the National Key R&D Program of China (No. 2018YFF0214705 ). Maosen Cao and Zhongqing Su are grateful for the support from the National Natural Science Foundation of China through Grant Nos. 11772115 and 51875492 , respectively. This work is also partially supported by the Natural Science Foundation of Jiangsu Province (No. BK20171439 ). Wei Xu is particularly grateful for the fellowship provided by the Hong Kong Scholars Program (No. XJ2018042 ).
Funding Information:
This work is supported by the National Key R&D Program of China (No. 2018YFF0214705). Maosen Cao and Zhongqing Su are grateful for the support from the National Natural Science Foundation of China through Grant Nos. 11772115 and 51875492, respectively. This work is also partially supported by the Natural Science Foundation of Jiangsu Province (No. BK20171439). Wei Xu is particularly grateful for the fellowship provided by the Hong Kong Scholars Program (No. XJ2018042).
Publisher Copyright:
© 2020
PY - 2021/2/3
Y1 - 2021/2/3
N2 - A fatigue crack that periodically opens and closes subject to a harmonic excitation can be referred to as a breathing crack. Higher harmonics generated by breathing cracks can manifest the occurrence of a crack. Although the modulation due to the opening–closing motion has been widely recognized as the cause of higher harmonics, the intrinsic force that drives a breathing crack to generate harmonics is not yet clear. With the objective of providing physical insights into the intrinsic force that generates harmonics, a novel concept of nonlinear pseudo-force (NPF) in the breathing crack is proposed in this study. The NPF is analytically formulated by rearranging the equation of transverse motion of a beam bearing a breathing crack, whose bending stiffness changes periodically during forced harmonic vibration. In a physical sense, the mechanism for generating higher harmonics is explicitly expounded using the NPF. In addition, the amplification effect of higher harmonics owing to differentiation is quantitatively investigated using multiple scenarios. The nonlinear behaviors of harmonics generated by breathing cracks are well explained using the NPF proposed in this study. A beam that bears a fatigue crack is taken as a specimen for experimental validation, whose steady-state velocity responses are acquired through non-contact vibration measurement. Finally, the application potential of the NPF for detecting and locating breathing cracks is explored. In particular, this study proposes a novel nonlinear approach for crack identification using the NPF, whose capability in detecting and locating breathing cracks is verified on beams with breathing cracks.
AB - A fatigue crack that periodically opens and closes subject to a harmonic excitation can be referred to as a breathing crack. Higher harmonics generated by breathing cracks can manifest the occurrence of a crack. Although the modulation due to the opening–closing motion has been widely recognized as the cause of higher harmonics, the intrinsic force that drives a breathing crack to generate harmonics is not yet clear. With the objective of providing physical insights into the intrinsic force that generates harmonics, a novel concept of nonlinear pseudo-force (NPF) in the breathing crack is proposed in this study. The NPF is analytically formulated by rearranging the equation of transverse motion of a beam bearing a breathing crack, whose bending stiffness changes periodically during forced harmonic vibration. In a physical sense, the mechanism for generating higher harmonics is explicitly expounded using the NPF. In addition, the amplification effect of higher harmonics owing to differentiation is quantitatively investigated using multiple scenarios. The nonlinear behaviors of harmonics generated by breathing cracks are well explained using the NPF proposed in this study. A beam that bears a fatigue crack is taken as a specimen for experimental validation, whose steady-state velocity responses are acquired through non-contact vibration measurement. Finally, the application potential of the NPF for detecting and locating breathing cracks is explored. In particular, this study proposes a novel nonlinear approach for crack identification using the NPF, whose capability in detecting and locating breathing cracks is verified on beams with breathing cracks.
KW - breathing crack
KW - crack identification
KW - Fatigue crack
KW - harmonics
KW - non-contact measurement
KW - nonlinear pseudo-force
UR - http://www.scopus.com/inward/record.url?scp=85094557368&partnerID=8YFLogxK
U2 - 10.1016/j.jsv.2020.115734
DO - 10.1016/j.jsv.2020.115734
M3 - Journal article
AN - SCOPUS:85094557368
SN - 0022-460X
VL - 492
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
M1 - 115734
ER -