Conical shells are of the most widely engineering structures and various studies have been conducted in the analysis of their behavior. They are widely used in generous engineering applications such as hoppers, vessel heads, components of missiles, spacecraft and marine vessels. Vibration analysis is one of the most important issues in the field. Nowadays in order to improve the behavior and properties of the shells, functionally graded materials (FGM) are used in their manufactures. Mechanical properties of them as non-homogeneous materials are changed continuously. Usually, these materials are made from ceramic and metal. The ceramic constituent of the material provides the high temperature resistance due to its low thermal conductivity. The ductile metal constituent prevents fracture caused by stresses due to high temperature gradient. In this research, free vibration of rotating functionally graded truncated conical shells is investigated. Vibration analysis is based on shell thickness using the theories of two-dimensional and three-dimensional for shells. For thin walled, moderately thick and thick conical shells are used the justify; LINE-HEIGHT: 115%; TEXT-INDENT: 14.2pt; MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none" Results show convergence of this method and compared with other published works. By several numerical solutions, the effects of material property graded index, angular velocity, Coriolis acceleration, geometrical parameters and boundary conditions on the natural frequency are investigated. Also the critical velocity in unstable condition is obtained. At the end, the results of these noted theories compared with each other. For thin-walled conical shells, each theory has sufficiently accurate. But in thick conical shells, the difference of natural frequency between ltr Keywords: Free vibration, Conical shells, Functionally Graded Materials, GDQ, Classical, First order shear deformation, Layerwise theory.
