Accurate natural frequencies and critical speeds of a rotating functionally graded moderately thick cylindrical shell

• We consider a rotating FG cylinder and we study the effect of rotational speed on its frequencies.
• The governing equations are based on first order shear deformation type sanders shell theory.
• An exact procedure is used to solve the equations for all of the classical boundary conditions.
• Geometrical and material properties of FG cylinder change the forward and backward frequencies trends.
• The critical speed of FG cylinder changes against material index with an interesting behavior.

This paper presents an exact analytical solution for free vibration of a rotating functionally graded circular cylindrical shell based on Sanders shear deformation theory. The state space method is employed to solve the problem. The equations of motion are extracted by considering Coriolis, centrifugal and initial hoop tension effects. Several comparison studies with results reported in literature as well as a finite element model are carried out, to demonstrate accuracy of the present new exact results. Effects of various combinations of boundary conditions, rotational speed, geometrical and material properties of the shell on the forward and backward waves of the natural frequencies are investigated. Also, variations of the critical speed versus material properties are discussed. Due to the inherent features of the present exact solution, the present findings will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods and can be utilized as a reliable reference by the other researchers.