Nonlinear vibration analysis of geodesically-stiffened laminated composite cylindrical shells in an elastic medium

Nonlinear free vibration and parametric resonance analysis for a geodesically-stiffened anisotropic laminated thin cylindrical shell of finite length subjected to static or periodic axial forces using the boundary layer theory is presented. The shell is embedded in an elastic medium which is modeled as a Pasternak elastic foundation. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The equations of motion are developed using the Donnel shell theory with a von Kármán-type of kinematic nonlinearity, and the shell-foundation interaction and the extension-shear, extension-flexural and flexural-twist couplings are included. A two-step perturbation technique is employed to determine the linear and nonlinear frequency and parametric resonance of the geodesically-stiffened anisotropic laminated cylindrical shells. The numerical analysis involves the nonlinear vibration behavior of laminated composite cylindrical shells with respect to the material properties and the influences of initial stress, geometric shell characteristics (i.e., radius, length and thickness, including geodesic, axial and ring stiffeners), and stacking sequence. The results reveal that the shell geometric parameters, elastic medium, and periodic axial excitation have a significant effect on the nonlinear vibration behavior of anisotropic laminated composite cylindrical shells.