Response of a loaded rectangular plate on fractional derivative viscoelastic foundation

Deformation of a loaded plate on soil foundation will normally exhibit considerable time-dependent behaviour. In this paper, a fractional derivative Kelvin model is proposed to study the quasi-static problem of a rectangular plate rested on a viscoelastic foundation, which is subjected to uniform distributed loads. According to the correspondence principle of elasticity and visco-elasticity, the elastic solution of this problem is extended to the fractional derivative viscoelastic solution in terms of the Mittag-Leffler function using Laplase transform. The study of an example indicates that the fractional derivative visco-elastic model is more adaptive than the classical viscoelastic model. The influence of the model parameters on the plate deflection-time relationship is studied through a parametric study. The analysis results indicate that the time-dependent deformation of the plate can be accurately captured by varying values of the fractional order of differential operator and the coefficient of viscosity.