Boundary layer theory for the nonlinear vibration of anisotropic laminated cylindrical shells

A boundary layer theory for the nonlinear flexural vibration of anisotropic shear deformable laminated cylindrical shells is developed. The shell may be embedded in an elastic medium that 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. Two kinds of fiber reinforced composite (FRC) laminated cylindrical shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity and including the extension-twist, extension-flexural and flexural-twist couplings. The thermal effects are also included, and the material properties of FRCs are estimated through a micromechanical model and are assumed to be temperature dependent. The equations of motion are solved by a singular perturbation technique to determine the linear and nonlinear frequencies of the FRC laminated cylindrical shells. The effects of material property gradient, the temperature change, shell geometric parameter, stacking sequence, foundation stiffness as well as the end conditions on the vibration characteristics of FRC shells are discussed in detail through a parametric study. The results show that a functionally graded reinforcement has a moderately effect on the linear and nonlinear vibration characteristics of FRC shells.