Free vibration analysis of nanotube-reinforced composite truncated conical shell resting on elastic foundation

In this paper, Free Vibration analysis of truncated conical shell Reinforced with single-walled carbon nanotubes for uniformly distribution (UD), resting on Pasternak elastic foundation, based on the first order shear deformation plate theory is investigated. The rule of mixture is used to effect of the properties of nanotubes in the mentioned structure. Based on the displacement field according to the first order shear deformation theory, after determining the strain components in the curvilinear coordinates and simplifying derived relation, we compute the strain components in conical coordinate. Then, the stress components are derived by the Hook’s law. In the next stage, by computing the total potential energy of system by regarding the effect of Pasternak elastic foundation and regarding the suitable functions for displacements, by applying the Ritz method the natural frequency of system have been derived. At the end, the effect of volume fraction of nanotubes, ratio of thickness to radius of cone, elastic constants and other parameters, on the natural frequency of structure have been investigated. Also, it can be observe close agreements between present results and other papers.