Assessment of theories for free vibration analysis of homogeneous and multilayered plates

Abstract

This paper assesses classical and advanced theories for free vibrational response of homogeneous and multilayered simply supported plates. Closed form solutions are given for thick and thin geometries. Single layer and multilayered plates made of metallic, composite and piezo-electric materials, are considered. Classical theories based on Kirchhoff and Reissner-Mindlin assumptions are compared with refined theories obtained by enhancing the order of the expansion of the displacement fields in the thickness direction z. The effect of the Zig-Zag form of the displacement distribution in z as well as of the Interlaminar Continuity of transverse shear and normal stresses at the layer interface were evaluated. A number of conclusions have been drawn. These conclusions could be used as desk-bed in order to choose the most valuable theories for a given problem.