Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory

In this paper, size-dependent equations of motion for functionally graded cylindrical shell were developed using shear deformation model and rotation inertia. Material properties of the shell were assumed as continuously variable along thickness, and consistent with the variation in the component's volume fraction based on power law distribution. To consider the size effect, modified couple stress theory in conjunction with first order shear deformation shell model were used, and general equations of motion and classical and non-classical boundary conditions were derived based on Hamilton's principle. Finally, in the special case, using the Navier procedure, the free vibrations of simply supported functionally graded cylindrical nanoshell were obtained, and the effects of parameters such as dimensionless length scale parameter, distribution of FG properties, thickness, and length on the natural frequency were identified and was compared with the classical theory. Results obtained through the modified couple stress theory are indicative of the considerable effect of the size parameter, particularly in bigger thicknesses and shorter lengths of nanotubes, on the natural frequency.