Orthotropic plates resting on viscoelastic foundations with a fractional derivative Kelvin-Voigt model

Abstract

The objective of this paper is to propose an analytical model for orthotropic plates resting on viscoelastic foundations using a fractional derivative Kelvin-Voigt model. The viscoelastic foundation offers the advantage of capturing time-dependent behavior. The incorporation of the fractional derivative enhances the accuracy of the model in predicting the viscoelastic response. The behavior of plate is described using classical plate theory, while the viscoelastic foundation is simulated by modifying the Kelvin-Voigt model. The governing equation is established by utilizing the principle of virtual work. The analytical solution of the simply supported rectangular plate is obtained applying Navier’s approach and the Mittag-Leffler function. Subsequently, the influences of the parameters involved in this model on the bending responses are thoroughly studied. The results reveal the following key findings: (1) the order of fractional derivative determines the characteristics of foundation, specially whether it exhibits elastic or viscoelastic behaviors; (2) the creep time controls both the rate of the incremental deflection and the position of characteristic point; and (3) the stiffnesses of the spring and springpot exert a dominant influence on the bending responses. Furthermore, numerical results calculated from the proposed analytical solution will serve as a benchmark for future research on numerical validation.