The fractional Kelvin-Voigt model for circumferential guided waves in a viscoelastic FGM hollow cylinder

Abstract

Abstract Compared to the traditional integer order viscoelastic model, a fractional order derivative viscoelastic model is shown to be more accurate. A thorough knowledge of the dispersive characteristics of such model is very essential to the application of guided wave testing technique. In this paper, the guided waves in a fractional Kelvin-Voigt viscoelastic FGM hollow cylinder with material changing in the thickness direction are investigated. The Weyl definition of fractional order derivatives and the extended Legendre polynomial approach are employed for the derivations of the governing equations. The presented approach has the advantage that the solution of the complex partial differential wave equations with variable coefficients is reduced to an eigenvalue problem, which overcomes the shortcomings of the existing iterative methods such as the Newton downhill method and improves computation efficiency. The previous methods for dealing with viscoelastic guided wave transform the wave equations into a matrix determinant problem solved by the iterative methods, which has a very slow calculation speed. Comparisons with the related studies are conducted to validate the correctness of the presented approach, and the convergence of the approach is discussed. The full three dimensional spectrum, phase dispersion curves and attenuation curves are illustrated for various fractional order viscoelastic FGM hollow cylinders. The influences of fractional order, grade field and radius-thickness ratio on dispersion and attenuation curves are illustrated. The difference of the dispersion characteristics between the viscoelastic model and the elastic one is discussed. The influences of fractional order on displacement distributions are also studied.