Free axisymmetric vibrations of heated non-uniform Bi-directional FGM Mindlin rings employing quadrature approaches

Abstract

The present article investigates the axisymmetric vibrations of non-uniform bi-directional functionally graded rings under two-dimensional temperature distribution on the basis of first-order shear deformation theory. The linear variation of thickness along the radial direction is controlled by a taper parameter. The temperature-dependent mechanical properties are assumed to be graded in thickness as well as radial direction. The separation of variables method is applied to obtain the classical solution of two-dimensional heat conduction equation by imposing the thermal boundary conditions. The governing differential equations of thermoelastic equilibrium and axisymmetric motion together with boundary conditions are extracted from Hamilton’s principle. The quadrature technique is used to obtain the frequency equations and then the lowest three roots of these equations are calculated by MATLAB. After validating the results for the present approach, numerical results are given to analyze the effects of thermal environment, taper parameter, volume fraction index, heterogeneity and density parameters on the frequency parameter. Mode shapes for the specified rings are illustrated.