Free vibration analysis of nanotube-reinforced composite conical shell in high temperature environment

In this research, free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) conical shells subjected to high temperature environment is investigated. The material properties of FG-CNTRC are assumed to be graded through the thickness direction. Two kinds of carbon nanotube reinforced composites including uniformly distributed (UD), CNTs are distributed uniformly through the shell thickness, and functionally graded (FG), CNTs are graded with three different distribution, are considered. The effect of thermal loading is considered as an initial stress. Applying the Hamilton’s principle based on classic theory and considering Von Karman strain-displacement relation, the governing equations are obtained. The analytical Galerkin method together with beam mode shapes as weighting functions is employed to solve the equations of motion. The results are compared with those presented in literature. In addition, the effect of various parameters such as thermal loading, boundary conditions, and different geometrical conditions are studied. It is shown that the initial thermal stresses have significant effects on the natural frequencies and cannot be neglected. Moreover, the critical buckling temperature rise of the shells can be extracted from the presented diagrams of the fundamental frequency parameters verses the temperature rise.