Effect of thermal environment on the asymmetric vibration of temperature-dependent two-dimensional functionally graded annular plate by Chebyshev polynomials

In the present paper, an accurate numerical technique is employed to analyze the effect of two-dimensional temperature variation on the free asymmetric vibrations of functionally graded (FG) annular plates using the first-order shear deformation theory. The temperature-dependent mechanical properties of the plate material are graded along the thickness and radial directions. The governing differential equations for asymmetric motion are derived from Hamilton's principle and the exact solution for the two-dimensional heat conduction equation is obtained using the separation of variables method considering thermal boundary conditions. The Chebyshev collocation technique is adopted to compute the numerical values of fundamental frequency for different boundary conditions. The impact of volume fraction index, heterogeneity parameter, density parameter, nodal lines, radii ratio, and thermal boundary conditions on the frequencies of the plate is investigated. An excellent agreement between the results obtained by the present approach and other methods available in the literature validated the authors' model and technique. Three-dimensional normalized mode shapes with different nodal lines are illustrated for the specified plates.