Third Order Formulation for Vibrating Non-Homogeneous Cylindrical Shells in Elastic Medium

Third order shear deformation theory of cylindrical shells is employed to investigate the vibration characteristics of non-homogeneous cylindrical shells surrounded by an elastic medium. The kinematic relations are obtained using the strain-displacement relations of Donnell shell theory. The shell properties are considered to be dependent on both position and thermal environment. A suitable function through the thickness direction is assumed for the non-homogeneity property. The Winkler-Pasternak elastic foundation is used to model the elastic medium. Analytical solutions are presented for cylindrical shells with simply supported boundary conditions. From the numerical studies, it is revealed that, the natural frequencies are affected significantly by the elastic foundation coefficients and environmental temperature conditions.