Investigation of guided waves propagation in orthotropic viscoelastic carbon–epoxy plate by Legendre polynomial method

• Effectiveness of the Legendre polynomial method for modeling the guided wave propagation in viscoelastic plate.
• Comparison of results obtained by both hysteretic and Kelvin–Voigt viscoelastic models.
• The effects of elastic and viscoelastic modulus on dispersion and attenuation curves.
• The specific advantages and disadvantages of the proposed Legendre polynomial method.

The effect of viscoelasticity on the guided waves propagation in viscoelastic plate has been investigated according to multi-aspect. To this purpose, an extension of the Legendre polynomial method is proposed to formulate the guided waves equation in orthotropic viscoelastic plate composed of carbon–epoxy. The validity of the proposed Legendre polynomial method is illustrated by comparison with available data. The convergence of the method is discussed through a numerical example. The hysteretic and Kelvin–Voigt viscoelastic models are used to integrate the imaginary part of the complex stiffness matrix associated with the viscoelastic plate in this study. Accordingly, both viscoelastic models do not affect on the dispersion curves results. However, appreciable effects are seen in the attenuation curves. Also, the sensitivity of the guided waves propagation caused by variations of elastic and viscoelastic modulus has been studied in detail. Finally, the advantages of the Legendre polynomial method are described.