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In this paper, the dynamics of a viscoelastic plate resting on a viscoelastic Winkler foundation and traversed by a moving mass is studied. The Laplace transform is employed to derive the governing equation of the problem. Thereafter, an analytical-numerical method is proposed in order to determine the dynamic response of the plate. The method is based on transforming the governing partial differential equation into a new solvable system of linear ordinary differential equations. To that extent, the proposed solution proves to be applicable to plates made of any viscoelastic material and with various boundary conditions. Moreover, the moving mass may travel at any arbitrary trajectory with... 

The stability of a viscoelastic plate strip, subjected to an axial load with the Kelvin–Voigt fractional order constitutive relationship is studied. Based on the classical plate theory, the structural formulation of the plate is obtained by using the Newton’s second law and the aerodynamic force due to the fluid flow is evaluated by piston theory. The Galerkin method is employed to discretize the equation of motion into a set of ordinary differential equations. To determine the stability margin of plate the obtained set of ordinary differential equations are solved using the Laplace transform method. The effects of variation of the governing parameters such as axial force, retardation time,...