Finite Element Method Applied to Supersonic Flutter of Circular Cylindrical Shells

Abstract

DOI: 10.2514/1.39580 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 approximatedbypolynomialfunctions.Pistontheorywithandwithoutacorrectionfactorforcurvatureisappliedto 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 dynamicinstability.Theresultsarecomparedwithexistingexperimentaldataandotheranalyticaland finiteelement 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. Nomenclature � A� = coefficient matrix of shape functions; see Appendix B.1 a1 = freestream speed of sound � B� = coefficient matrix of strain vector; see Eq. (11) � Cf� = global aerodynamic damping matrix � cf�