Chapter 12 Simulating Nonlinear Beating Phenomena Induced by Dry Friction in Dynamic Systems Iyabo G. Lawal, Michael R. Haberman, and Keegan J. Moore Abstrac t Self-excitation and beating phenomena are the result of nonlinear constitutive behavior of vibrating structures with nonlinear components. These behaviors require externally supplied excitation and can be induced by the combination of near equilibrium damping and nonlinear damping operating far from equilibrium. In this study, dry friction, a mechanism known for producing self-excitation in structures, is explored as a mechanism for producing beat phenomena in structures. The system consists of two masses connected via a linear spring with one of the masses damped via a grounded dashpot that is modeled using a five-parameter friction contact model. The system is modeled and solved using the RK-4 time-integration scheme. We perform system parameter identification of experimental data using the STFT (short-time Fourier transform) and wavelet-bounded empirical mode decomposition (WBEMD) to determine system model variables that may simulate the selfexcitation and beat phenomena observed in the structural dynamics. Beat phenomena may also be a result of the existence of two or more closely separated damped natural frequencies. We also investigate the degree to which self-excitation in the structure is driving the nonlinear beat phenomenon as opposed to it being caused by choosing closely separated damped natural frequencies. We address this question using nonlinear normal modes (NNM) analysis which provides frequencyenergy dependence of the modes as system parameters change. The approach developed here is useful for the design of energy harvesting and vibration isolation systems that are subjected to sliding friction. Keyword s Beating phenomena · Empirical mode decomposition · Friction · Mode lock-in · Self-excitation 12.1 Introduction The emergence of “beating” has been observed in structures and depends on their stiffness and damping properties. In several studies, “beating” phenomena has been observed to be a result of closely separated modes in the structure, which in a linear system would produce a similar effect. It could also be caused by harmonic interactions driven by nonlinearities in the contact interface or by self-excitation within the structure. The root cause of this “beating” phenomena is not yet fully understood. The motivation in modeling this phenomena is to understand what set of parameters generate this effect in a 2-DOF mass system that consists of a driven linear oscillator and a nonlinear module with damping elements. This configuration of elements has also been known to produce targeted energy transfer (TET) from the linear oscillator to the strongly nonlinear module, known as a nonlinear energy sink (NES) [1, 2]. Kerschen and others [1] found that “beat phenomena” was a more efficient means of energy transfer than the reliance of either fundamental or sub-harmonic resonance capture. The efficiency of energy pumping or one-way energy transfer increases when “beating” phenomena is present. Another self-excitation effect is caused by friction-induced vibrations, where substructures separated by frictional contacts create self-excitation in the overall structure and in some cases may produce “brake squeal” [3]. This phenomena is identified as “mode lock-in” by the structural dynamics community. Prior studies explore how viscous elements can produce passive energy suppression in structures [4]. In this work, we explore another angle, by looking at friction as a dissipative element for TET. Friction has the I. G. Lawal ( ) · M. R. Haberman Department of Mechanical Engineering, University of Texas at Austin, Austin, TX, USA e-mail: iyabo@utexas.edu; haberman@utexas.edu K. J. Moore Department of Mechanical & Materials Engineering, University of Nebraska–Lincoln, Lincoln, NE, USA e-mail: kmoore@unl.edu © The Society for Experimental Mechanics, Inc. 2024 M. R. W. Brake et al. (eds.), Nonlinear Structures & Systems, Volume 1 , Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-36999-5_12 93
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