An analytical model is presented to predict the influence of nonlinearities associated with supersonic fluid flow on the dynamic and stability behavior of thin isotropic cylindrical shells. The method developed is a combination between finite element method, sander’s shell theory and nonlinear aerodynamic theory (third-order piston theory). The shell is subdivided into cylindrical finite elements, the displacements functions are derived from exact solutions of Sanders equations for thin cylindrical shells and the influence of stress stiffening due to internal or external pressure and axial compression is also taken into account. Expressions for the masse and stiffness matrices are determined by exact analytical integration. With the nonlinear dynamic pressure, we develop nonlinear matrices: stiffness, damping and coupling matrices for flow. The nonlinear equation of motion is then solved using a fourth-order Runge-kutta numerical method. Frequency variations are determined with respect to the amplitude of the motion for different cases. This is a powerful model to predict linear, nonlinear vibrations and stability characteristics of cylindrical shells subjected to external supersonic flow that can be applied for the aeroelastic design of aerospace vehicles.
Hybrid finite element method in supersonic flutter analysis of circular cylindrical shells
