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2024 | OriginalPaper | Chapter

7. Systems with Contact Nonlinearities

Author : Malte Krack

Published in: Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics

Publisher: Springer Nature Switzerland

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Abstract

This chapter focuses on exploiting contact nonlinearities. Dry friction and unilateral contact are ubiquitous in science and technology. Their effect cannot be properly described in a linearized way. Dry friction is often the main cause for dissipation in structural dynamics. Impulsive unilateral interactions (impacts) are ideal for cross-scale energy transfer. Contact is easy to practically realize, but the dynamics of mechanical systems undergoing contact interactions is challenging to accurately predict. This chapter is divided into friction damping, a self-adaptive system and impact absorbers. Besides illustrating the use of strong nonlinearity in those engineering applications, this chapter presents useful methodology, including predictive modeling and numerical computation techniques, and the concept of Nonlinear Modes.

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previous chapter Hysteretic Systems: Resonances, Modal Coupling, Mitigation

The name Vibro-Impact Nonlinear Energy Sink (VI-NES) is now frequently used for the impact damper (Gendelman, 2012; Lamarque et al., 2011; Vakakis et al., 2008). The impact damper dates back at least to the 1930s (Paget, 1937). In contrast, the concept of the NES and the theoretical framework for its analysis was only recently proposed in Vakakis et al. (2008).

This inherent limitation of tuned vibration absorbers applies to any passive concept that requires–by careful design–tuning to the system’s natural frequencies in order to achieve effective energy transfer. Examples are the conventional linear tuned-mass damper (Den Hartog, 1985), and the nonlinear tuned vibration absorber (Detroux et al., 2015), both of which exploit natural frequency matching (1:1 internal resonance) between the host structure and the absorber, and targeted energy transfer into sacrificial modes by exploiting sub- or super-harmonic internal resonances (see e.g. Krack et al., 2015; Quaegebeur et al., 2022).

Provided that the absorber is not placed at a vibration node, the sign of \(\boldsymbol{\varphi }\) can be selected without loss of generality such that \(\varphi _{\mathrm c}\) is positive.

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Title: Systems with Contact Nonlinearities
Author: Malte Krack
Publisher: Springer Nature Switzerland
Book: Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics
Print ISBN: 978-3-031-56901-2

Electronic ISBN: 978-3-031-56902-9

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-56902-9_7