Second-Order Elastic Airplane Models

Normal mode analysis deals with linearized structural models. In particular, a non­linear coupling between rigid-body angular velocity and elastic deformations is neglected in normal mode analysis. However, this coupling shows up if one goes back to first prin­ciples in the derivation of the elastic modes by energy methods. Technically, the vector cross-product of assumed small deformations and large deformation rates is a neglected nonlinear effect. Another refinement that is neglected in ordinary normal mode analysis is the axial strain resulting from transverse deformation of the structure as a beam.

Nonlinear aeroelastic formulations that include these effects have been studied by aero­elastic investigators such as Carey S. Buttrill, Luigi Morino, R. K. Cavin, and A. R. Dusto. While nonlinear effects are conceded to be significant for the modal analysis of flexible spacecraft, the need for this sophistication is uncertain for airplanes (Buttrill, 1989).