Geometrically nonlinear oscillations of composite sandwich cylindrical shell with honeycomb core under axial time periodic force

Cylindrical composite sandwich shell, which consists of two outer layers and thick honeycomb core, is considered. The outer thin layers are manufactured from composite orthotropic material and honeycomb core is manufactured from orthotropic plastic. Parametric nonlinear oscillations of cylindrical shell under the action longitudinal time periodic force are considered. The honeycomb core is homogenized. As a result, orthotropic solid continuum is obtained. Stressed state of every layer is described by higher order shear theory, which uses five generalized displacements (three displacements projections and two rotations angles of normal to middle surfaces). The assumed-mode method is applied to obtain the system of nonlinear ordinary differential equations with respect to the generalized coordinates to describe the sandwich structure vibrations. The shooting technique and continuation method are applied jointly to analyze the nonlinear oscillations, their stability and bifurcations. The geometrically nonlinear oscillations are considered in the principal parametric resonances with account of internal resonances. Stability and bifurcations of periodic motions are shown on the frequency response, which describes the structure nonlinear dynamics in principle parametric resonances.