Three-dimensional free vibration of thick functionally graded annular plates in thermal environment

Abstract

The free vibration analysis of functionally graded (FG) thick annular plates subjected to thermal environment is studied based on the 3D elasticity theory. The material properties are assumed to be temperature dependent and graded in the thickness direction. Considering the thermal environment effects and using Hamilton's principle, the equations of motion are derived. The effects of the initial thermal stresses are considered accurately by obtaining them from the 3D thermoelastic equilibrium equations. The differential quadrature method (DQM) as an efficient and accurate numerical tool is used to solve both the thermoelastic equilibrium and free vibration equations. Very fast rate of convergence of the method is demonstrated. Also, the formulation is validated by comparing the results with those obtained based on the first-order shear deformation theory and also with those available in the literature for the limit cases, i.e. annular plates without thermal effects. The effects of temperature rise, material and geometrical parameters on the natural frequencies are investigated. The new results can be used as benchmark solutions for future researches.