First-Order Frequency Effects in Supersonic Panel Flutter of Finite Cylindrical Shells

An improved calculation of the supersonic panel flutter characteristics of a thin cylindrical shell of finite length is presented. The aerodynamic load is determined with account taken of first-order terms in vibration frequency, and when this is introduced into the elastic shell equation an integro differential equation results. An equivalent eigenvalue problem is set up by applying Galerkin’s method to this equation. The flutter boundary, for given Mach number and circumferential mode n, corresponds to the shell thickness ratio at which the real part of any one of the eigenvalues first becomes non-negative. It is found that the most severe flutter condition, for given Mach number, occurs for a circumferential mode n = 7. The present calculations exclude second-order frequency terms in the elastic part of the flutter equation, even though they may have a first-order effect. A subsequent calculation referred to here shows that these terms indeed have no significant influence on the first-order analysis.