A shear deformable conical shell formulation in the framework of couple stress theory

In this paper, the governing equations of the conical shell are derived by using the first-order shear deformable shell model and taking into account the size parameter through couple stress theory. In order to obtain the governing equations, Hamilton’s principle is used and the equations of shell motion with partial differentials are derived along with classical and non-classical boundary conditions. Finally, the free vibration of the single-walled carbon nanocone (SWCNC) is scrutinized through examples. The SWCNC is modeled as simply supported, and the Galerkin method is used to solve the vibration problem. The results of the new model are compared with those of the classical theory, which point to the conclusion that the classical model is a special case of couple stress theory. Results also reveal that nanoshell rigidity in the couple stress theory is greater than that in the classical theory, which leads to an increase in natural frequencies. Moreover, the study investigates the effect of the size parameter on nanoshell vibration for different lengths and apex angles.