Chapter21 Experimental Study of Isolated Response Curves in a Two-Degree-of-Freedom Nonlinear System T. Detroux, J.P. Noël, G. Kerschen, and L.N. Virgin Abstract In the present paper, the observation and characterization of isolated response curves (IRCs) are experimentally reported in the case of a nonlinear system consisting of two masses sliding on an horizontal guide. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the complete system is imposed by prescribing the displacement of their supports. The existence of an IRC is related to a 3:1 internal resonance between the two modes of the system. The observed IRC is studied in detached and merged conditions using swept-sine excitations and system perturbations. Keywords Isolated response curve • Internal resonance • Experimental observation • Two-degree-of-freedom system • Sine-sweep excitation • Perturbations 21.1 Introduction Isolated response curves (IRCs) are an intriguing feature of nonlinear dynamics. They correspond to closed loops of solutions emerging in nonlinear frequency responses and which are, by definition, detached from the main response branch [1]. IRCs may thus go easily undetected in the analysis of the forced response of a nonlinear system, whether it be numerically employing classical continuation techniques, or experimentally applying sine-sweep excitations. However, an increase in forcing amplitude may cause the merging of the main branch and the IRC, resulting in dramatic frequency and amplitude shifts of the resonance location. This renders IRCs potentially dangerous in practice for engineers designing systems likely to operate in nonlinear regimes of motion [2, 3]. In [4], the authors investigated numerically a series of intrinsic features of IRCs, in particular their creation mechanism, the evolution of their bifurcations according to parameter variations and their basins of attraction. In the present paper, the observation and characterization of IRCs are experimentally reported in the case of a two-degree-of-freedom, base-excited mechanical system with nonlinear hardening springs. As it is conjectured that interactions between nonlinear modes underlie the existence of IRCs [5, 6], potential 3:1 internal resonances between the in-phase and out-of-phase modes of the system are specifically studied. Section 21.2 details the experimental setup of interest. In Sect. 21.3, the forced response of the setup to swept-sine excitations of various amplitudes is analyzed. The existence of an IRC is revealed through the sudden shift undergone by the resonance frequency of the in-phase mode. Perturbations are also applied to the system to observe the IRC when detached. Conclusions of the paper are summarized in Sect. 21.4. 21.2 An Experimental Two-Degree-of-Freedom System with Hardening Springs The experimental setup consists of two masses sliding on an horizontal guide, as shown in Fig. 21.1a, b. The masses are connected together and to the ground through extension springs, whose lengths and stiffnesses determine the static equilibrium of the system. Motion of the masses is recorded by means of uniaxial accelerometers. Two transverse bungee T. Detroux • J.P. Noël ( ) • G. Kerschen Aerospace and Mechanical Engineering Department, Space Structures and Systems Laboratory, University of Liège, Liège, Belgium e-mail: jp.noel@ulg.ac.be L.N. Virgin Nonlinear Dynamics Group, School of Engineering, Duke University, Durham, NC, USA © The Society for Experimental Mechanics, Inc. 2016 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29739-2_21 229
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