Non-linear vibrations and instabilities of orthotropic cylindrical shells with internal flowing fluid

In this work, Donnell’s non-linear shallow shell equations are used to study the dynamic instability of perfect simply supported orthotropic cylindrical shells with internal flowing fluid and subjected to either a compressive axial static pre-load plus a harmonic axial load or a harmonic lateral pressure. The fluid is assumed to be non-viscous and incompressible and the flow, isentropic and irrotational. An expansion with eight degrees of freedom, containing the fundamental, companion, gyroscopic, and four axi-symmetric modes is used to describe the lateral displacement of the shell. The Galerkin method is used to obtain the non-linear equations of motion which are solved by the Runge–Kutta method. A detailed parametric analysis clarifies the influence of the orthotropic material properties on the non-linear buckling and vibration characteristics of the shell. Numerical methods are used to identify the effect of the fluid flow and applied loads control parameters on the bifurcations and stability of the shell motions.