Computation of nonlinear normal modes of large structures: application to a full-scale aircraft

Summary. The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) ofcomplex real-world structures is now within reach. The application considered in this study is the airframe of the Morane-SaulnierParis aircraft, whose ground vibration tests exhibited some nonlinear structural behaviors. The NNMs are computed using a numericalalgorithm combining shooting and pseudo-arclength continuation. Introduction Nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlineardynamical phenomena, yet they have a clear and simple conceptual relation to the LNMs [1, 2, 3]. However, moststructural engineers still view NNMs as a concept that is foreign to them, and they do not yet consider NNMs as a usefulconcept for structural dynamics. One reason supporting this statement is that most existing constructive techniques forcomputing NNMs are based on asymptotic approaches and rely on fairly involved mathematical developments.In this paper, we support that numerical algorithms pave the way for an effective and practical computation of NNMs.The proposed algorithm, implemented in MATLAB, relies on two main techniques, namely a shooting procedure anda method for the continuation of NNM motions. We show that the numerical computation of the NNMs of complexreal-world structures, such as the finite element model of the full-scale aircraft studied herein, is then within reach.