Transonic Panel Flutter Predictions Using a Linearized Stability Formulation

Abstract

A methodology is presented for prediction of dynamic instabilities arising from fluid–structure coupling. The inviscid compressible Euler equations are linearized about a steady-state solution and converted to the frequency domain for evaluation of the unsteady generalized aerodynamic forces used in the flutter solution procedure. The coupled fluid–structure interaction problem is formulated as a linearized stability eigenvalue problem. Using Schur complement factorization, an assumption of harmonic frequency response, and projection onto the structural modal basis, the stability equations are rewritten in a form well known as the flutter solution method. The scheme is used to study the flutter instability boundary of simply supported semi-infinite and square panels in the transonic and low supersonic region for mass ratio 0.1. The critical instability at subsonic Mach numbers is divergence (zero frequency), whereas oscillatory unstable modes are found for all Mach numbers greater than 1.0. At low supersonic Mach numbers ( for semi-infinite panel and for square panel), multiple high-frequency flutter modes become critical in a very narrow range of dynamic pressures. For higher Mach numbers, the classic supersonic flutter mode is recovered for both panels.