The Possio Integral Equation of Aeroelasticity: A Modern View

  • A. V. Balakrishnan
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 199)

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.

keywords

Possio Equation AeroElasticity Instability Wing Flutter 

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Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • A. V. Balakrishnan
    • 1
  1. 1.Department of Electrical EngineeringUniversity of CaliforniaLos AngelesUSA

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