Response for a Loaded Rectangular Plate on Viscoelastic Foundation with Fractional Derivative Model

According to the Pasternak elastic foundation, a fractional derivative model for viscoelastic foundation is derived, and the equations of elastic and viscoelastic rectangular loaded plate on viscoelastic foundation with the fractional derivative Kelvin model are established. The dynamic equations of elastic and viscoelastic rectangular plate with four edges simply supported are solved by using the Galerkin method and the segmented numerical method. Then, the accuracy of the solution is verified by the case of free vibration. Besides, the influences of the fractional order, viscosity parameter, horizontal shear coefficient, and modulus parameter on the displacement of rectangular plate under dynamic load are analyzed. The results show that the fractional derivative model is able to describe the mechanical characteristics of viscoelastic material; the displacement of rectangular plate appears different attenuation before and after the fractional order is 0.5, and the attenuation speed of the displacement increases with the increasing of the viscosity parameter, horizontal shear parameter, and modulus parameter.