A concept of complex-wavelet modal curvature for detecting multiple cracks in beams under noisy conditions

Abstract

Detection of multiple damage using modal curvature in noisy environments has become a research focus of considerable challenge and great significance over the last few years. However, a noticeable deficiency of modal curvature is its susceptibility to noise, which usually results in a noisy modal curvature with obscured damage signature. To address this deficiency, this study formulates a new concept of complex-wavelet modal curvature. Complex-wavelet modal curvature features the ability to reveal and delineate damage under noisy conditions. The effectiveness of the concept is analytically verified using cracked beams with various types of boundary conditions. The applicability is further experimentally validated by an aluminum beam with a single crack and a carbon-fiber-reinforced polymer composite beam with three cracks in the laboratory with mode shapes measured by a scanning laser vibrometer. Both analytical and experimental results have demonstrated that the complex-wavelet modal curvature is capable of revealing slight damage by eliminating noise interference, with no need for prior knowledge of either material properties or boundary conditions of the beam under inspection.