The Equation of Energy Balance for Fluttering Systems with Some Applications in the Supersonic Regime

IT IS WELL KNOWN that the development of a critical flutter oscillation can be attributed to the existence, at an appropriate air speed, of a right (characteristic) set of amplitude ratios and phase angles (eigenmodes) between certain component motions—being then neutrally stable, the system is potentially capable of energy gain (or loss) as a result of some further perturbation. It seems natural then that a study of the eigenmodes, rather than the eigenvalues (critical flutter speed and frequency parameter) should lead to a clearer understanding of the flutter mechanism and of those system parameters which are most significant in allowing it. This is indeed the case; and it will be shown how such a study leads to some useful tools of assessment for the practicing aeroelastician. The emphasis in analysis here passes from interest in the solution, by whatever means, of the characteristic flutter determinant for the eigenvalues to an assessment of the eigenmodes which is best made by consideration of the equation of energy balance. This, in turn, illuminates the equations of motion themselves so that a cursory inspection of the matrices of the flutter coefficients can be very revealing as to the system behavior and stability. Such assessment as is possible with the concepts outlined below provides a useful guide in formulating and interpreting conventional flutter analyses.