Spectral finite element method analysis of dispersion characteristics of guided wave in anisotropic composite plates

Spectral finite element method is introduced to study the dispersion and the mode shape of guided waves in layered anisotropic composite plates. Based on the three-dimensional elastodynamic equation, the dispersion equation is obtained by finite-element-discretization of the cross-section of the waveguide alone. The displacements along the wave propagation direction are also described in an analytical fashion as harmonic exponential functions. The dispersion curves and the mode shape of guided waves that propagate in different directions of single-layer and double-layer composite plates have been analyzed. The effect of the thickness ratio of the bi-layered composite plates to the phase velocity of the basic modes is discussed. The results showed that the symmetric mode is characterized by weak dispersion along the fiber direction in a wide frequency range. The phase velocity of basic modes is greatly influenced by the thickness ratio of bi-layered composite plates at low frequencies, and is closer to the lower phase velocity of the material with the increase of frequency. The study provides a theoretical basis of guided waves for quantitatively non-destructive testing and performance evaluation of composite materials.