Free Vibration Analysis of Functionally Graded Nano Graphene Composite Sandwich Plates Resting on a Winkler-Pasternak Foundation

The free vibrations of graphene-reinforced composite sandwich plates resting on a Winkler-Pasternak foundation were analyzed. The sandwich structure was divided into three layers including two thin facesheets made of a functionally graded graphene-reinforced composite and a thick core from a soft lightweight polymer foam. Five different functionally graded distribution patterns were considered for the facesheets. A refined high order theory was employed for kinematic assumptions. The transverse flexibility of the core and zero transverse shear stress conditions at the lower and upper surfaces of the plate were taken into account. The Hamilton’s principle was used to obtain the equations of motion and the analytical solutions were presented. Effects of the elastic foundation, plate geometry, and the graphene platelets properties on the natural frequencies of the sandwich plate were explored. The accuracy and reliability of the present modeling and results were examined and verified in specific cases. Results showed that reinforcing the facesheets of sandwich plates by graphene platelets increases their natural frequencies.