Fractional calculus approach for bending of viscoelastic plate using two-variable refined plate theory

This paper deals with the time-dependent bending behavior of a rectangular viscoelastic plate based on the two-variable refined plate theory using the fractional calculus approach. The plate is fully simply-supported and is subjected to uniformly-distributed loading and the three-parameter merchant model is used for simulation of viscoelastic behavior. The time-domain governing equations are converted into frequency-domain ones using the Laplace transform and then, these equations are solved by the Navier method. The viscoelastic plate response is obtained using the elastic-viscoelastic correspondence principle so that the response of an elastic equivalent problem is extended into the viscoelastic problem. The results of this study, including plate deflection, and in-plane and transverse strains are compared with the results of the elastic model and the standard merchant model where the comparison of obtained results with the reference ones shows that the proposed approach has good accuracy. Also, the variation of deflection through the plate thickness and the effect of aspect ratio on the results are studied. This study shows that the proposed fractional model has the ability to simulation of both elastic and viscose effects simultaneously which is more compatible with the nature of viscoelastic materials.