Continuum Aeroelastic Model for Inviscid Subsonic Bending-Torsion Wing Flutter

A full continuum aeroelastic model for bending-torsion dynamics of a slender high-aspect-ratio wing in inviscid subsonic airflow is developed avoiding finite element or Padé approximations. The structure model is the classical cantilever model of Goland. The aerodynamics is simplified to the two-dimensional typical section theory. Stability is discussed in the Laplace domain leading to the calculation of the aeroelastic modes, the stability curve, and a precise definition of flutter speed, as well as an explicit formula for divergence speed. The flutter speed is shown to be monotonic decreasing as $M$ increases for small $k$ (normalized complex frequency); if a mode flutters at $M=0$ then it flutters for every $M>0$ excepting $M=1$ . A time-domain state space model is developed requiring the language of abstract functional analysis in the form of a “convolution-evolution” equation in a Hilbert space. The time domain model for $M=0$ differs radically from $0<M⩽1$ . It helps clarify the nature of the aeroelastic modes and flutter instability. The state space model can be used for control design including self-straining actuators.