Local variation detection in MDOF system using wavelet based transmissibility and its application in cracked beam

Since the local stiffness or damping variation happens when damage occurs in engineer structures, it is useful to detect the local variation as a way for structural damage inspection. As a vibration based approach, transmissibility has attracted considerable interest because of its convenience and effectiveness in damage detection. However, using the traditional Fourier transform, it should be very careful to select the frequency bands in transmissibility calculation. Inappropriate choice of frequency band could cause a complete inaccurate result. For unknown damage detection, it is difficult to select the frequency band which eigen-frequency should be included. This paper proposes a novel method using wavelet based transmissibility for local variation detection. Benefiting from the ability in subtle information acquisition of wavelet transform, it is useful in reducing the influence of frequency bands to the indicators. Analytical derivation using wavelet balance method and numerical studies of a multiple degree of freedom (MDOF) system are carried out to verify the effectiveness of the proposed method. In the last section, the method is applied for detecting crack position in cantilever beam with analysis of its sensitivity to frequency bands and measurement inaccuracies.