Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule

In the present paper, free axisymmetric vibrations of functionally graded circular plates subjected to a non-linear temperature distribution along the thickness direction have been studied on the basis of classical plate theory. The top and bottom surfaces of the plate are under uniform thermal environment. The mechanical properties of the plate material are assumed to be temperature-dependent and the plate is graded in thickness direction. The equations for thermo-elastic equilibrium as well as axisymmetric motion for such a plate model have been derived using Hamilton's principle. Employing generalized differential quadrature rule, the numerical values of thermal displacements from thermo-elastic equilibrium equation and frequencies from the equation of motion for the lowest three modes of vibration have been computed for clamped, simply supported and free plates. The effects of the temperature difference at the surfaces together with material graded index and thickness of the plate on the frequencies have been investigated. The benchmark results for uniform and linear temperature distributions have been computed. For the validity of present considerations and the technique, frequency parameter has been compared for some special cases with published results obtained from other approximate methods. (C) 2019 Elsevier Ltd. All rights reserved.