Fourier spectral-based modal curvature analysis and its application to damage detection in beams

In this paper, a simple Fourier spectral-based method is proposed to calculate the modal curvature (MC) of beams instead of the traditional central difference method. Based on the present method, damages in beam-like structures are localized. The present method provides an alternative selection to estimate MC in damage detection. There are two advantages of the present method. Firstly, the spectral calculation of spatial derivatives is conducted globally, which provides the suppression for noise. In addition, signal processing in the wavenumber domain provides an alternative choice for spatial filtering for mode shapes. Secondly, the proposed method provides a precise estimation of the MC which is related to original definition. With the absence of numerical derivative, the estimated results can be more stable and robust. Statistical analysis is conducted to show the effectiveness and noise immunity of the proposed method. In order to obtain the better identification, the MC calculated by the proposed method is employed as the input of continuous wavelet transform, and then the hybrid method is generated. The validations of the present method and comparison with the traditional central difference method are numerically and experimentally demonstrated.