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.