Thermal effect on free vibration of ring-stiffened rotating functionally graded conical shell with clamped ends

An approximate solution is presented to investigate the effects of thermal load on the frequency of ring-stiffened rotating functionally graded conical shell. Material properties and the temperature field are assumed to be graded and varied in the thickness direction. The shell is reinforced by equal interval rings. The equations of motion are derived by the Hamilton's principle. Approximate analytical solutions are assumed to satisfy clamped boundary conditions, and then Fourier decomposition and Galerkin method are applied to achieve relations of frequencies. To validate, the comparisons are made with a number of particular cases in literature and with the FEM solutions.