An analytical model incorporating a combination of the finite element method, Sanders-Koiter nonlinear shell theory and third-order piston theory is presented in this paper to study the influence of nonlinearities associated with structure geometry and supersonic fluid flow on the dynamic and flutter instability behavior of thin anisotropic cylindrical shells. The shell is subdivided into cylindrical finite elements and the displacement functions are derived from exact solutions of Sander’s equations for thin cylindrical shells. These functions are treated using the finite element method, which is developed to determine the linear and nonlinear mass and stiffness matrices of the structure. The internal and external pressure and axial compression are taken into account. All expressions of founding matrices are determined by exact analytical integration.

By applying the nonlinear dynamic pressure, which represents the effect of nonlinearities of supersonic fluid flow on cylindrical shells, the linear and nonlinear matrices for stiffness, damping and coupling are found. The nonlinear equation of motion is then solved using a fourth-order Runge-Kutta numerical method. Nonlinear vibrations are determined with respect to the amplitude of vibrations and thickness ratio for different cases. This approach leads to the development of a powerful model capable of predicting linear, nonlinear vibrations and flutter instability of cylindrical shells subjected to external supersonic flow. One specific application of this model is the aeroelastic design of aerospace vehicles. This research is part of a series of current studies in the literature that tackle the effects of the nonlinearity of external supersonic fluid flow on cylindrical shells; an area of study that has been neglected by most research to-date.

geometric nonlinearities, fluid flow nonlinearities, cylindrical shells, supersonic flow, finite element method, flutter instability.