Parametric Resonance of a Three-Layered Cylindrical Composite Rib-Stiffened Shell*

Equations for the parametric resonance of a three-layered cylindrical shell with composite layers stiffened with ribs and containing a hollow isotropic cylinder are obtained. The shell is loaded by axial forces and an external pressure varying harmonically in time. The influence of the cylinder is modeled as an elastic foundation whose modulus of subgrade reaction was determined from equations of 3D elasticity theory. Their solution is sought in the form of a trigonometric series in the axial coordinate. The infinite system of inhomogeneous differential equations of Mathieu-Hill type obtained is solved using a trigonometric series in time. Using a numerical example, the main regions of instability were obtained for the first time, and plots for the critical frequencies on the channel radius, the elastic modulus of cylinder material, and the number and height of ribs are found. The mathematical model proposed extends the range of relevant scientific and applied problems in studying three-layered stiffened shells.