Introducing Legendre wavelet functions for damage detection in laminated composite beams

This paper introduces Legendre wavelets as a novel wavelet type and explores their effectiveness in detecting damage in carbon-epoxy composite beams. These wavelets are generated by differentiating the first derivative of Legendre functions on a ten-digit grid using finite difference methods, resulting in three versions with seven, five, and three sampling points. The Legendre wavelet functions with five and three sampling points are computed. Carbon-epoxy laminated composite beam mode shapes serve as the input signal for a Legendre wavelet transform. Numerical and experimental studies validate the practical applicability of these wavelets for damage detection. Results demonstrate that all Legendre wavelet functions are suitable for damage detection in laminated composite beams. Especially, those derived from higher-degree Legendre polynomials exhibit superior performance.