Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory

Vibration of functionally graded sandwich (FGS) cylindrical nanoshell is investigated. For this purpose, the first shear deformable shell theory as well as material length scale parameter as considered by the couple stress theory is used, and Hamilton's principle is employed to derive the equations of motion of the FGS cylindrical nanoshell and the boundary conditions. In the end, using Navier solution, the natural frequency is determined for three types of FGS cylindrical nanoshells. Results of the new model are compared with the classical theory. According to the results, the rigidity of the FGS cylindrical nanoshell in the couple stress theory is higher than that in the classical theory, which leads to increased natural frequency. Besides, the effect of the material length scale parameter on natural frequency of the FGS cylindrical nanoshell in different wavenumbers and lengths is considerable.