Vibration analysis of functionally graded plates using the eight-unknown higher order shear deformation theory in thermal environments

Abstract

This paper deals with free vibration of functionally graded material plates using eight-unknown higher order shear deformation theory in thermal environments. The theory is based on full twelve-unknown higher order shear deformation theory, simultaneously satisfies zero transverse shear stress at the top and bottom surfaces of the FG plate. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. Equations of motion are derived from Hamilton's principle. The accuracy of present analytical solution is confirmed by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated.