Nonlinear Normal Modes of a Full-Scale Aircraft M. Peeters, G. Kerschen, J.C. Golinval Structural Dynamics Research Group Department of Aerospace and Mechanical Engineering University of Lie` ge, Lie` ge, Belgium E-mail: m.peeters, g.kerschen, jc.golinval@ulg.ac.be C. Ste´phan, P. Lubrina Office National d’Etudes et de Recherches Ae´rospatiales (ONERA) DADS-ADSE Chaˆ tillon, France E-mail: cyrille.stephan, pascal.lubrina@onera.fr ABSTRACT The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft, whose ground vibration tests have exhibited some nonlinear structural behaviors. The finite element model of this aircraft, elaborated from drawings, has more than 80000 degrees of freedom, and softening nonlinearities exist in the connection between the external fuel tanks and the wing tips. From this model, a reduced-order model, which is accurate in the [0-100Hz] range, is constructed using the CraigBampton technique. The NNMs of the reduced model are then computed using a numerical algorithm combining shooting and pseudo-arclength continuation. The results show that the NNMs of this full-scale structure can be computed accurately even in strongly nonlinear regimes and with a reasonable computational burden. Nonlinear modal interactions are also highlighted by the algorithm and are discussed. 1 INTRODUCTION Nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the LNMs [1−3]. However, most structural engineers still view NNMs as a concept that is foreign to them, and they do not yet consider NNMs as a useful concept for structural dynamics. One reason supporting this statement is that most existing constructive techniques for computing NNMs are based on asymptotic approaches and rely on fairly involved mathematical developments. There have been very few attempts to compute NNMs using numerical methods[4−7]. Algorithms for the continuation of periodic solutions are really quite sophisticated and advanced (see, e.g., [8−10]), and they have been extensively used for computing the forced response and limit cycles of nonlinear dynamical systems (see, e.g., [11]). Interestingly, they have not been fully exploited for the computation of nonlinear modes. In this paper, we support that these 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 and a method for the T. Proulx (ed.), Modal Analysis Topics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series 6, 223 DOI 10.1007/978-1-4419-9299-4_19, © The Society for Experimental Mechanics, Inc. 2011
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