Two-dimensional modal curvature estimation via Fourier spectral method for damage detection

Modal curvature is one of the most important damage indices utilized in the damage identification for composite structures. However, few kinds of sensors can provide the measure for modal curvature directly. The lack of direct measurement method for modal curvature necessitates the use of the central difference estimation, which reduces the stability of the algorithm. Noise is severely amplified by the central difference, and hence limits the damage identification through the use of modal curvature estimation. Instead of numerical differentiation, the two-dimensional Fourier spectral method is employed to conduct the two-dimensional modal curvature estimation in this paper. The use of Fourier spectral method over the conventional central difference operator gives the proposed methodology the following advantages: (1) Spectral calculations for spatial derivatives are implemented in global space, thus noise can be suppressed. The k-domain generated in algorithm provides the space for spatial filtering. (2) The precise estimation for modal curvatures can be obtained by aid of the trigonometric interpolation in spectral method. (3) The proposed method calculates the modal curvatures based on fast Fourier transform, thus the efficiency is ensured. By the numerical and experimental comparisons with the classical central difference method, the suitability of the present method is verified for composite structures.