NON-HOPFIAN TRANSONIC FLUTTER

摘要

A critical analysis of the theoretical foundation of the Hopf bifurcation as a model for transonic flutter is presented. Our objective is to show that certain nonlinear transonic flutter instabilities cannot be described using the Hopf theory. The breakdown occurs because the unsteady aerodynamic forces cannot be linearized without introducing nonuniformities in time or space. Consequently, the Hopf linearization also breaks down, and a uniformly valid Jacobian matrix whose eigenvalues normally determine flutter stability no longer exists. This in turn implies that these flutter instabilities cannot be predicted by formulating and solving a classical linear aeroelastic eigenvalue problem, nor can the Hopf bifurcation serve as a model for describing the corresponding nonlinear flutter boundary.