The fractional Kelvin-Voigt model for Rayleigh surface waves in viscoelastic FGM infinite half space

Abstract

In this paper, we use the fractional Kelvin-Voigt model to investigate the propagation behavior of Rayleigh waves along the surface of viscoelastic functionally graded material (FGM) half space. Fractional derivatives combing with the power series technique are for the first time employed for the derivations of the governing equations. The influences of the viscous parameter, integer order, and fractional order derivative variations on Rayleigh wave dispersion relations are discussed. Numerical results show that the viscous parameter has little effect on the dispersion relations and attenuation curves of the Rayleigh waves in infinite half space. Furthermore, the rule regarding the trend of attenuation curves for various types of modes are studied when the Rayleigh wave is in normal dispersion. In general, the attenuation in the first mode is very small, so we can omit it. Moreover, the second mode is significantly different from other higher order modes in numerical value and rule of change. These results may provide theoretical guidance for the fabrication of new materials and the nondestructive evaluation in engineering applications, and might also serve to explain some phenomena surrounding seismic wave propagation.