Nonlinear vibration localisation in a symmetric system of two coupled beams
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ORIGINAL PAPER
Nonlinear vibration localisation in a symmetric system of two coupled beams Filipe Fontanela . Alessandra Vizzaccaro . Jeanne Auvray . Bjo¨rn Niedergesa¨ß . Aure´lien Grolet . Loı¨c Salles . Norbert Hoffmann
Received: 6 January 2020 / Accepted: 10 June 2020 Ó The Author(s) 2020
Abstract We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental investigation employing two weakly coupled beams touching against stoppers for large vibration amplitudes confirms the nonlinear localisation. Keywords Vibration localisation Symmetry breaking bifurcation Clearance nonlinearity
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11071-020-05760-x) contains supplementary material, which is available to authorized users. F. Fontanela A. Vizzaccaro (&) L. Salles N. Hoffmann Imperial College London, Exhibition Road, London SW7 2AZ, UK e-mail: [email protected] J. Auvray Ecole Centrale Marseille, 13451 Marseille Cedex 20, France B. Niedergesa¨ß N. Hoffmann Hamburg University of Technology, 21073 Hamburg, Germany A. Grolet Ecole Nationale Superieure d’Arts et Me´tiers ParisTech, 59000 Lille, France
1 Introduction The emergence of localised vibration in symmetric structures is a challenging problem in the aerospace industry due to high cycle fatigue [6, 16, 25]. Usually, aerospace structures such as bladed-disks, antennas, and reflectors are composed of ideally identical substructures assembled in a symmetric configuration. In the linear regime, localisation may arise due to structural inhomogeneities originating in the manufacturing process or due to wear [1, 2]. In the aerospace industry, especially in the bladed-disk community, the phenomenon is thus widely referred to as a mistuning problem. The topic has attracted considerable attention in the literature, and research has mainly focused on effective numerical tools for prediction, experimental investigation, and the use of intentional mistuning during design stages [3, 4, 13, 14, 24]. However, in some cases, due to inherent nonlinear phenomena, the assumption of linear vibration might be misleading. In the case of structural dynamics, nonlinearity may arise, e.g. due to friction induced by internal joints, or vibro-impacts [18]. It is also known that the emergence of localised vibration might be provoked by nonlinear effects, as an alternative to the linear localisation mechanisms in mistuning [23]. For example, even perfectly symmetric structures may experience localised vibrations due to the dependence of mode shapes on amplitude, or due to bifurcations. However, most of the available knowledge on this
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kind of nonlinear vibration localisation relies on results from minimal models, and only few experimental studies have attempted to demonstrate the
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