THE EFFECT OF SMALL SCALE ON THE FREE VIBRATION OF FUNCTIONALLY GRADED TRUNCATED CONICAL SHELLS

摘要

In this paper, the FG thin truncated conical shell formulation is developed using the modified couple stress theory. The material distributions in FG conical shell are assumed to vary continuously along shell thickness according to volume fraction of constituents based on power law distribution. The governing equations and boundary conditions are derived using Hamilton's principle, and, in the special case, the free vibration of the simply supported FG conical nanoshell is investigated using Galerkin method. Finally, the effects of parameters such as dimensionless length scale parameter, apex angle, gradient index and length on the natural frequency are examined. According to the studies conducted, the modified couple stress theory predicts the stiffness of conical nanoshell with higher accuracy than the classical continuum theory. Besides, the increasing effect of the length scale parameter on increase in natural frequency caused by decrease in length and increase in circumferential and axial wave numbers is investigated as well.