The Possio integral equation of aeroelasticity: A modern view

Abstract

A central problem of AeroElasticity is the determination of the speed of the aircraft corresponding to the onset of an endemic instability known as wing 'flutter'. Currently all the effort is completely computational: wedding Lagrangian NASTRAN codes to the CFD codes to produce 'Time Marching' solutions. While they have the ability to handle nonlinear complex geometry structures as well as viscous flow, they are based approximation of the p.d.e. by o.d.e., and restricted to specified numerical parameters. This limits generality of results and provides little insight into phenomena. And of course are inadequate for Control Design for stabilization. Retaining the continuum models,we can show that the basic problem is a Boundary Value/Control problem for a pair of coupled partial differential equations, and the composite problem can be cast as a nonlinear Convolution/Evolution equation in a Hilbert Space. The Flutter speed can then be characterized as Hopf Bifurcation point, and determined completely by the linearised equations. Solving the linearised equations is equivalent to solving a singular integral equation discovered by Possio in 1938 for oscillatory response.In this paper we examine the Equation and its generalizations from the modern mathematical control theory viewpoint. © 2006 International Federation for Information Processing.