Nonlinear Modal Analysis of a Full-Scale Aircraft

Abstract

Nonlinear normal modes, which are defined as a nonlinear extension of the concept of linear normal modes, are a rigorous tool for nonlinear modal analysis. The objective of this paper is to demonstrate that the computation of nonlinear normal modes and of their oscillation frequencies can now be achieved for complex, real-world aerospace structures. The application considered in this study is the airframe of the Morane–Saulnier Paris aircraft. Ground vibration tests of this aircraft exhibited softening nonlinearities in the connection between the external fuel tanks and the wing tips. The nonlinear normal modes of this aircraft are computed from a reduced-order nonlinear finite element model using a numerical algorithm combining shooting and pseudo-arclength continuation. Several nonlinear normal modes, involving, e.g., wing bending, wing torsion, and tail bending, are presented, which highlights that the aircraft can exhibit very interesting nonlinear phenomena. Specifically, it is shown that modes with distinct linear frequencies can interact and generate additional nonlinear modes with no linear counterpart.