Vibrational damage detection using fractal surface singularities with noncontact laser measurement

摘要

This study concerns damage detection in plate-type structures using fractal surface singularities with noncontact laser measurement of structural dynamic responses. The fractal dimension analysis aided by linear isomorphism is used to deal with mode shapes for a plate with damage. With this method, the linear isomorphism is utilized to remove the local extrema while preserving the damage information of a mode shape, giving a retrofitted mode shape. The retrofitted mode shape is processed by Katz's fractal dimension analysis to produce a fractal dimension surface with its singular peak indicating the presence and location of the damage. In the method, a series of high-resolution mode shapes of the plate are used, which are acquired by using a noncontact measurement system consisting of a piezoceramic transducer as the actuator and a scanning laser vibrometer as the sensor. The capability of the method to locate and quantify damage is numerically demonstrated using a two-side-clamped aluminum plate with cracks of various depths; the efficacy of the method in identifying complex cracks is experimentally validated using a suspended aluminum plate bearing a cross-like crack. The numerical and experimental results show that the proposed method can accurately identify complex damage in plates, requiring neither benchmark models for the entire structure under investigation, or any prior knowledge of the material properties and the boundary conditions of the structure.