Investigation of Viscoelastic Guided Wave Properties in Anisotropic Laminated Composites Using a Legendre Orthogonal Polynomials Expansion-Assisted Viscoelastodynamic Model.

This study investigates viscoelastic guided wave properties (e.g., complex-wavenumber-, phase-velocity-, and attenuation-frequency relations) for multiple modes, including different orders of antisymmetric, symmetric, and shear horizontal modes in viscoelastic anisotropic laminated composites. To obtain those frequency-dependent relations, a guided wave characteristic equation is formulated based on a Legendre orthogonal polynomials expansion (LOPE)-assisted viscoelastodynamic model, which fuses the hysteretic viscoelastic model-based wave dynamics and the LOPE-based mode shape approximation. Then, the complex-wavenumber-frequency solutions are obtained by solving the characteristic equation using an improved root-finding algorithm, which leverages coefficient matrix determinant ratios and our proposed local tracking windows. To trace the solutions on the dispersion curves of different wave modes and avoid curve-tracing misalignment in regions with phase-velocity curve crossing, we presented a curve-tracing strategy considering wave attenuation. With the LOPE-assisted viscoelastodynamic model, the effects of material viscosity and fiber orientation on different guided wave modes are investigated for unidirectional carbon-fiber-reinforced composites. The results show that the viscosity in the hysteresis model mainly affects the frequency-dependent attenuation of viscoelastic guided waves, while the fiber orientation influences both the phase-velocity and attenuation curves. We expect the theoretical work in this study to facilitate the development of guided wave-based techniques for the NDT and SHM of viscoelastic anisotropic laminated composites.