Dynamic analysis of heated temperature-dependent bi-directional advanced composites circular plates with quadratic thickness variation

Abstract

Analysis and numerical results for the axisymmetric vibrations of non-uniform two-dimensional functionally graded circular plates subjected to two-directional temperature distribution are presented on the basis of the exact neutral surface and Mindlin plate theory. The mechanical properties of the plate material are supposed to be temperature-dependent and graded in thickness as well as in radial direction. Based on the thermal boundary conditions, a classical solution of the two-directional heat conduction equation is obtained by the separation of variables method. Equations for thermoelastic equilibrium and axisymmetric motion of the plate are derived in the framework of Hamilton’s principle. The numerical solution of these equations is carried out by the generalized differential quadrature method to compute the thermally induced displacements and natural frequencies using MATLAB. The lowest three values are reported as the frequency parameter for the first three modes of clamped and simply-supported plates. To show the influence of the exact neutral surface, taper parameters, material graded index, heterogeneity and density parameter, numerical results are presented. Mode shapes are plotted for the specified plates.