Free vibration analysis of plates taking into account rotary inertia and shear deformation via three alternative theories: a Lévy-type solution

This paper deals with the exact calculation of natural frequencies of a plate with two opposite edges simply supported considering three versions of the Uflyand–Mindlin plate theory: the original Uflyand–Mindlin plate theory, the truncated version of this model as suggested by Elishakoff, and the recently proposed Uflyand–Mindlin plate theory based on slope inertia. The comparison between the frequencies using the different models and with those found in the literature using numerical methods shows the efficiency of the models and the methods presented hereinafter.