Free vibration analysis of functionally graded rotating conical shells in thermal environment

Due to the wide applications of functionally graded shells in high temperature conditions, the study of dynamic behavior of these structures in thermal conditions is of the key importance. The vibration of rotating functionally graded conical shells with temperature-dependency of material properties is studied in this paper. The Donnel shell theory is employed to extract governing equations including initial thermomechanical stresses as well as centrifugal forces, Coriolis forces, and initial hoop tensions due to rotation. The initial thermomechanical stresses are obtained from the nonlinear heat conduction equation with temperature-dependent thermal conductivity for temperature distribution and linear bending equations for initial deflections. The method of generalized differential quadrature is employed to solve the problem. The obtained results are compared with the available literature and finally, the effects of angular velocities, thermal conditions, volume fraction index, semi vertex angles and lengths of the cone on frequency are investigated.