Chapter 15 Experimental Demonstration of a 3D-Printed Nonlinear Tuned Vibration Absorber C. Grappasonni, G. Habib, T. Detroux, and G. Kerschen Abstract Engineering structures are designed to be lighter and more flexible, hence reducing the extent of application of linear dynamic models. Concurrently, vibration mitigation is required for enhancing the performance, comfort or safety in real-life applications. Passive linear vibration absorbers are purpose-built, often designed using Den Hartog’s equal-peak strategy. However, nonlinear systems are known to exhibit frequency-energy-dependent oscillations which linear absorbers cannot effectively damp out. In this context, the paper introduces a new nonlinear tuned vibration absorber (NLTVA) whose nonlinear functional form is tailored according to the frequency-energy dependence of the nonlinear primary structure. The NLTVA design aims at ensuring equal peaks in the nonlinear receptance function for an as large as possible range of forcing amplitudes, hence generalizing Den Hartog’s method to nonlinear systems. Our focus in this study is on experimental demonstration of the NLTVA performance using a primary structure consisting of a cantilever beam with a geometrically nonlinear component at its free end. The absorber is implemented using a doubly-clamped beam fabricated thanks to 3D printing. The NLTVA performance is also compared with that of the classical linear tuned vibration absorber. Keywords Nonlinear resonances • Tuned vibration absorber • Equal-peak method • 3D printing • Experimental demonstration 15.1 Introduction Engineering structures must often operate in a harsh dynamic environment. Passive vibration absorbers have therefore been exploited to mitigate the resonant vibrations with a limited increase in weight. Linear tuned vibration absorbers (LTVA) are commonly designed using the well-established Den Hartog’s equal-peak strategy [1]. However, in view of its narrow bandwidth, the LTVA can be ineffective when the primary structure exhibits frequency-energy-dependent nonlinear oscillations. In this context, a nonlinear counterpart to the classical LTVA would be extremely beneficial, and several nonlinear absorbers have been proposed in the literature, see, e.g., [2–5]. The concept of a nonlinear tuned vibration absorber (NLTVA) was introduced by the authors in [6]. One unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog’s equalpeak method. In the present study, the NLTVA effectiveness is verified experimentally on a primary structure consisting of a cantilever beam with a geometrically nonlinear component at its free end. The procedure that we propose herein to design and validate the NLTVA is sketched in Fig. 15.1. Starting from an experimentally-characterized structure, an equivalent nonlinear single-degree-of-freedom (SDOF) modal model of the targeted resonance is first derived (Sect. 15.2). From the nonlinear modal model, the analytic tuning procedure developed in [6] provides the absorber’s parameters, and, in particular, its load-deflection characteristic (Sect. 15.3). The NLTVA is then implemented using doubly-clamped geometrically nonlinear beams which are fabricated using 3D printers. The mechanical and geometrical properties of the nonlinear beams are also obtained analytically (Sect. 15.4). Finally, the NLTVA performance is verified experimentally through sine sweep testing at different excitation levels (Sect. 15.5). C. Grappasonni ( ) • G. Habib • T. Detroux • G. Kerschen Space Structures and Systems Laboratory (S3L), Department of Aerospace and Mechanical Engineering, University of Liège, Liège, Belgium e-mail: chiara.grappasonni@ulg.ac.be; giuseppe.habib@ulg.ac.be; tdetroux@ulg.ac.be; g.kerschen@ulg.ac.be © The Society for Experimental Mechanics, Inc. 2016 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15221-9_15 173
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