Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink
Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink
We consider a model of a vibro-impact nonlinear energy sink (VI-NES), where a ball moves within a cavity of an externally forced mass, impacting either end of the cavity. These impacts result in energy transfer from the mass to the ball, thus limiting the oscillations of the larger system. We develop a semi-analytical map-based approach, recently used for an inclined impact pair model, in the setting where there is energy transfer between the mass and the ball. With this approach we analytically derive exact expressions for the full dynamics of the VI-NES system without restricting the range of parameters, in contrast to other recent work in which an approximate reduced model is valid only for small mass of the ball, small amplitude, and a limited frequency range. We develop the bifurcation analysis for the full VI-NES system, based on exact maps between the states at successive impacts. This analysis yields parameter ranges for complex periodic responses and stability analyses for O(1) mass of the ball, forcing frequencies that are not the same as the natural frequency, and large amplitude forcing. The approach affords the flexibility to analytically study the dynamics of different periodic solutions and their stability, including a variety of impact sequences in the full two degree-of-freedom model of VI-NES. Comparisons of quantities that characterize the energy transfer point to the significance of different types of periodic behavior, which may occur for different parameter combinations. Our semi-analytical results also provide the impact phase, which plays an important role in the efficiency of the energy transfer.
Bifurcation, Impact map, Nonlinear sink, Targeted energy transfer, Vibro-impact
Liu, Ruofeng
6200c7f0-4a22-4162-b68b-1b9bb259c78c
Kuske, Rachel
eb2504e2-25b3-4838-8c59-8fe8eaecf443
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
15 May 2023
Liu, Ruofeng
6200c7f0-4a22-4162-b68b-1b9bb259c78c
Kuske, Rachel
eb2504e2-25b3-4838-8c59-8fe8eaecf443
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
Liu, Ruofeng, Kuske, Rachel and Yurchenko, Daniil
(2023)
Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink.
Mechanical Systems and Signal Processing, 191, [110158].
(doi:10.1016/j.ymssp.2023.110158).
Abstract
We consider a model of a vibro-impact nonlinear energy sink (VI-NES), where a ball moves within a cavity of an externally forced mass, impacting either end of the cavity. These impacts result in energy transfer from the mass to the ball, thus limiting the oscillations of the larger system. We develop a semi-analytical map-based approach, recently used for an inclined impact pair model, in the setting where there is energy transfer between the mass and the ball. With this approach we analytically derive exact expressions for the full dynamics of the VI-NES system without restricting the range of parameters, in contrast to other recent work in which an approximate reduced model is valid only for small mass of the ball, small amplitude, and a limited frequency range. We develop the bifurcation analysis for the full VI-NES system, based on exact maps between the states at successive impacts. This analysis yields parameter ranges for complex periodic responses and stability analyses for O(1) mass of the ball, forcing frequencies that are not the same as the natural frequency, and large amplitude forcing. The approach affords the flexibility to analytically study the dynamics of different periodic solutions and their stability, including a variety of impact sequences in the full two degree-of-freedom model of VI-NES. Comparisons of quantities that characterize the energy transfer point to the significance of different types of periodic behavior, which may occur for different parameter combinations. Our semi-analytical results also provide the impact phase, which plays an important role in the efficiency of the energy transfer.
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Accepted/In Press date: 24 January 2023
e-pub ahead of print date: 8 February 2023
Published date: 15 May 2023
Additional Information:
Funding Information:
The authors gratefully acknowledge partial funding for this work from NSF-CMMI, USA 2009270 and EPSRC, UK EP/V034391/1 .
Publisher Copyright:
© 2023
Keywords:
Bifurcation, Impact map, Nonlinear sink, Targeted energy transfer, Vibro-impact
Identifiers
Local EPrints ID: 484903
URI: http://eprints.soton.ac.uk/id/eprint/484903
ISSN: 0888-3270
PURE UUID: 8da5c553-8f95-4c8a-b800-7e3d1a261b7f
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Date deposited: 24 Nov 2023 17:33
Last modified: 18 Mar 2024 04:04
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Contributors
Author:
Ruofeng Liu
Author:
Rachel Kuske
Author:
Daniil Yurchenko
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