Nonlinear Aeroelasticity: Continuum Theory, Flutter/Divergence Speed, and Plate Wing Model

Abstract

This paper formulates flutter/divergence instability problems using continuum models for structure and air flow as coupled nonlinear partial differential equations. The structure model is a Kirchoff CFFF thin plate allowing for nonzero thickness and camber bending. The aerodynamics is modeled by the transonic small disturbance potential equation. The aeroelastic boundary conditions are derived for nonzero angle of attack. A central result is the time domain model as a nonlinear convolution/evolution equation in a Hilbert space. Flutter speed is characterized as a Hopf bifurcation point, completely determined by the linearized equations. The main tool in solving the linear equations is the Possio equation for nonzero angle of attack. Divergence speed is shown to be determined by an eigenvalue problem for linear operators. The corresponding stationary (steady state) solutions are more regular in the transonic range (as M goes to one) if the angle of attack is nonzero.