Free vibration analysis of FG-CNTRC cylindrical shells surrounded by elastic foundation subjected to thermal loading

In this paper, free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells surrounded by elastic foundation and subjected to uniform temperature rise loading 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) and functionally graded (FG) are considered. The elastic foundation is modeled by two-parameter Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effect of thermal loading is considered as a initial stress. Applying the Hamilton’s principle based on first-order shear deformation theory and considering Sanders and Donnell strain-displacement relation, the governing equations are obtained. Using the generalized differential quadrature method in axial direction and periodic differential matrix operators in circumferential direction, the equilibrium equations are discretized. The results are compared with those presented in literature. In addition, the effect of various parameters such as thermal loading, boundary conditions, elastic foundation and different geometrical conditions are studied. The results show that increase in the elastic foundation coefficients and initial thermal loading increase and decrease the non-dimensional fundamental frequency, respectively.