Analysis of conical shells in the framework of coupled stresses theory

In this paper, the thin conical shell model is developed by using the modified couple stress theory. This non-classical formulation can incorporate size effects in nano/micro scales. For this purpose, the thin shell model is used along with the modified couple stress theory, and the equations of motion with partial differentials and classical and non-classical boundary conditions are derived by using Hamilton’s principle. Finally, the free vibrations of the single-walled carbon nanocone (SWCNC) are examined as a special case. The SWCNC is modeled as simply supported, and the Galerkin method is used to solve the vibrational problem. Results of the new formulation are compared to the classical theory. The results show that nanoshell rigidity is greater in the modified couple stress theory than in the classical theory, which leads to an increase in the natural frequencies. Also, the effect of size parameter on the vibration frequency of SWCNC in different lengths and apex angles is examined.