Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs
Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs
A combined analysis of smooth and non-smooth bifurcations captures the interplay of different qualitative transitions in a canonical model of an impact pair, a forced capsule in which a ball moves freely between impacts on either end of the capsule. The analysis, generic for the impact pair context, is also relevant for applications. It is applied to a model of an inclined vibro-impact energy harvester device, where the energy is generated via impacts of the ball with a dielectric polymer on the capsule ends. While sequences of bifurcations have been studied extensively in single- degree-of-freedom impacting models, there are limited results for two-degree-of-freedom impacting systems such as the impact pair. Using an analytical characterization of impacting solutions and their stability based on the maps between impacts, we obtain sequences of period doubling and fold bifurcations together with grazing bifurcations, a particular focus here. Grazing occurs when a sequence of impacts on either end of the capsule are augmented by a zero-velocity impact, a transition that is fundamentally different from the smooth bifurcations that are instead characterized by eigenvalues of the local behavior. The combined analyses allow identification of bifurcations also on unstable or unphysical solutions branches, which we term ghost bifurcations. While these ghost bifurcations are not observed experimentally or via simple numerical integration of the model, nevertheless they can influence the birth or death of complex behaviors and additional grazing transitions, as confirmed by comparisons with the numerical results. The competition between the different bifurcations and their ghosts influences the parameter ranges for favorable energy output; thus, the analyses of bifurcation sequences yield important design information.
Energy harvesting, Fold bifurcation, Grazing bifurcation, Impact pair, Non-smooth dynamics, Period doubling bifurcation, Periodic solutions, Vibro-impact system
6129-6155
Serdukova, Larissa
a7d03a66-73fe-4265-9ce7-8ffdf334bc40
Kuske, Rachel
eb2504e2-25b3-4838-8c59-8fe8eaecf443
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
April 2023
Serdukova, Larissa
a7d03a66-73fe-4265-9ce7-8ffdf334bc40
Kuske, Rachel
eb2504e2-25b3-4838-8c59-8fe8eaecf443
Yurchenko, Daniil
51a2896b-281e-4977-bb72-5f96e891fbf8
Serdukova, Larissa, Kuske, Rachel and Yurchenko, Daniil
(2023)
Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs.
Nonlinear Dynamics, 111, .
(doi:10.1007/s11071-022-08152-5).
Abstract
A combined analysis of smooth and non-smooth bifurcations captures the interplay of different qualitative transitions in a canonical model of an impact pair, a forced capsule in which a ball moves freely between impacts on either end of the capsule. The analysis, generic for the impact pair context, is also relevant for applications. It is applied to a model of an inclined vibro-impact energy harvester device, where the energy is generated via impacts of the ball with a dielectric polymer on the capsule ends. While sequences of bifurcations have been studied extensively in single- degree-of-freedom impacting models, there are limited results for two-degree-of-freedom impacting systems such as the impact pair. Using an analytical characterization of impacting solutions and their stability based on the maps between impacts, we obtain sequences of period doubling and fold bifurcations together with grazing bifurcations, a particular focus here. Grazing occurs when a sequence of impacts on either end of the capsule are augmented by a zero-velocity impact, a transition that is fundamentally different from the smooth bifurcations that are instead characterized by eigenvalues of the local behavior. The combined analyses allow identification of bifurcations also on unstable or unphysical solutions branches, which we term ghost bifurcations. While these ghost bifurcations are not observed experimentally or via simple numerical integration of the model, nevertheless they can influence the birth or death of complex behaviors and additional grazing transitions, as confirmed by comparisons with the numerical results. The competition between the different bifurcations and their ghosts influences the parameter ranges for favorable energy output; thus, the analyses of bifurcation sequences yield important design information.
Text
s11071-022-08152-5
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More information
Accepted/In Press date: 29 November 2022
e-pub ahead of print date: 15 December 2022
Published date: April 2023
Additional Information:
Funding Information:
This work was supported by NSF-CMMI 2009270 and EPSRC EP/V034391/1 Grants.
Funding Information:
The authors gratefully acknowledge partial funding for this work from NSF-CMMI 2009270 and EPSRC EP/V034391/1.
Keywords:
Energy harvesting, Fold bifurcation, Grazing bifurcation, Impact pair, Non-smooth dynamics, Period doubling bifurcation, Periodic solutions, Vibro-impact system
Identifiers
Local EPrints ID: 484897
URI: http://eprints.soton.ac.uk/id/eprint/484897
ISSN: 0924-090X
PURE UUID: 6328b5b0-e585-4c38-adec-e907d05f014e
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Date deposited: 24 Nov 2023 17:31
Last modified: 18 Mar 2024 04:04
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Author:
Larissa Serdukova
Author:
Rachel Kuske
Author:
Daniil Yurchenko
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