TY - JOUR

T1 - Damage detection of cantilever beams based on derivatives of mode shapes

AU - Guo, Jin Quan

AU - Ou, Fen Lan

AU - Zhong, Jian Feng

AU - Zhong, Shun Cong

AU - Yang, Xiao Xiang

AU - Yao, Li Gang

PY - 2014/1

Y1 - 2014/1

N2 - For the small crack detection (crack ration less than 5%), the derivatives of mode shapes of cantilever beams were used for crack detection in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small discontinuity in the response at the crack location. It is hard to detect small cracks in beams using the direct data of mode shape change. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked cantilever beam provide a progressively better indication of the presence of a crack. However, `noise' effects due to the difference approximation error also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives of mode shapes. For the intact beam, these derivatives are smooth curves. So the local peaks or discontinuity on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and intact cantilever beams used were computed using the finite element method.

AB - For the small crack detection (crack ration less than 5%), the derivatives of mode shapes of cantilever beams were used for crack detection in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small discontinuity in the response at the crack location. It is hard to detect small cracks in beams using the direct data of mode shape change. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked cantilever beam provide a progressively better indication of the presence of a crack. However, `noise' effects due to the difference approximation error also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives of mode shapes. For the intact beam, these derivatives are smooth curves. So the local peaks or discontinuity on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and intact cantilever beams used were computed using the finite element method.

KW - damage detection

KW - small crack

KW - derivatives of mode shapes

U2 - 10.4028/www.scientific.net/AMM.488-489.817

DO - 10.4028/www.scientific.net/AMM.488-489.817

M3 - Article

VL - 488

SP - 817

EP - 820

JO - Applied Mechanics and Materials

JF - Applied Mechanics and Materials

SN - 1660-9336

ER -