Finite Element Method Applied to Supersonic Flutter of Circular Cylindrical Shells

摘要

The method of analysis is a combination of Sander's thin shell theory and the classic finite element method, in which the nodal displacements are found from the exact solution of shell governing equations rather than approximated by polynomial functions. Piston theory with and without a correction factor for curvature is applied to derive aerodynamic damping and stiffness matrices. The influence of stress stiffness due to internal pressure and axial loading is also taken into account. Aeroelastic equations in hybrid finite element formulation are derived and solved numerically. Different boundary conditions of the shell, geometries, and flow parameters are investigated. In all study cases, the shell loses its stability due to coupled-mode flutter and a traveling wave is observed during this dynamic instability. The results are compared with existing experimental data and other analytical and finite element solutions. The present study shows efficient and reliable results that can be applied to the aeroelastic design and analysis of shells of revolution in aerospace vehicles.