Transient response of rectangular plate on viscoelastic foundation under time-variable load based on fractional-order differential model (Q6058600)

The transient responses of a rectangular thin plate with a pair of edges simply supported and a pair of edges clamped, which is mounted on a viscoelastic foundation modeled by the fractional-order standard linear solid model, under rectangular pulse and ramp step loads are studied in this paper. The complex natural frequency and mode shape of the thin plate are obtained by solving the fractional-order differential equation. The analytic expression of the displacement response in term of Mittag-Leffler function is derived for the forced vibration under the rectangular pulse and ramp step load by the mode superposition method and the fractional-order Laplace transformation method. The semi-numerical solution and the complete numerical solution are provided in the numerical examples and compared with the analytic solution to cross-validate the reliability. The different effects of the fractional orders and the viscosity coefficients on the transient responses are also obtained. Extensive numerical data is presented in tabular and graphical form. The authors state that `it can be seen that the transient displacement response obtained in the present work is in good agreement with the published results in the literature and therefore, the analytic solution obtained in the present work is reliable'. In the opinion of the reviewer making such a statement is rather vague.