Free vibration analysis of orthotropic plates by differential transform and Taylor collocation methods based on a refined plate theory

Based on the two-variable refined plate theory, free vibration of orthotropic plates is analyzed using the differential transform method (DTM) and the Taylor collocation method (TCM). The refined plate theory outperforms the classical plate theory, and its formulation is simpler than those of other higher-order theories. Without the need for any shear correction factor, the theory performs reliably. The plates considered have two opposite edges simply supported (Levy plates). The first part of the analysis considers three combinations of clamped, simply supported and free edge conditions for the other two edges, keeping one of them simply supported. Detailed formulations of DTM and TCM for the free vibration analysis are given and, consequently, used to predict the frequency parameters and the effect of various factors ranging from geometric to material parameters. Next, the paper presents analysis of some cases, the multi-span plates and plates with stepped thickness and end rotational springs, whose analytical solutions are not readily available, particularly based on the two-variable refined plate theory. In order to verify the results, formulations of three more plate theories, namely the classical or Kirchhoff plate theory, the first-order shear deformation theory of Mindlin and the high-order shear deformation theory of Sayyad and Gugal, were implemented and solved using the proposed methods.