Damage detection in cantilever beams using spatial Fourier coefficients of augmented modes

A mode shape based damage detection method for a cantilever beam is proposed in this paper. The idea involves use of spatial Fourier series expansion of mode shapes. Mode shapes of a cantilever beam are not periodic in nature. However, by taking their mirror image about the fixed end, an augmented periodic mode can be created which permits spatial Fourier analysis. It is observed using finite element simulations that damage has a considerable impact on the spatial Fourier coefficients of the mode shapes of a damaged beam. It is also found that the Fourier coefficients are sensitive to intensity of damage and its location on the beam. Sensitivity of the Fourier coefficients in presence of noise is also analyzed and they are found to be effective in indicating the damage.