Non-linear vibration of composite orthotropic cylindrical shells on the non-linear elastic foundations within the shear deformation theory

Present study deals with the non-linear vibration of orthotropic cylindrical shells on the nonlinear elastic foundations. To account for the large deformations of the orthotropic cylindrical shell, von-Karman type of geometrical nonlinearity is included into the formulation. The shear deformation theory (SDT) is used to obtain the basic equations of orthotropic cylindrical shells on the nonlinear elastic foundations within the Donnell's shell theory. The superposition and Galerkin methods are adopted to convert the above equations into a nonlinear ordinary differential equation. The frequency-amplitude relationships for orthotropic cylindrical shells on the nonlinear elastic foundations in the framework of the SDT are obtained in the form of Jacobi elliptic function. The validity of the present method is demonstrated by comparing the present results with those available in the literature. Moreover, some new results are also presented for the nonlinear frequency parameters of the cylindrical shells to study effects of non-linear elastic foundations, vibration amplitude, shear stresses, orthotropy and shell characteristics.