Classification of periodic solutions in a single-degree-of-freedom system with backlash

Bart Besselink; Amit Shukla; Rob Fey; Henk Nijmeijer

doi:10.1115/DETC2007-34236

Classification of periodic solutions in a single-degree-of-freedom system with backlash

Bart Besselink, Amit Shukla, Rob Fey, Henk Nijmeijer

Onderzoeksoutput › Academic › peer review

2 Citaten (Scopus)

Samenvatting

In this paper a single degree-of-freedom system with backlash is studied for its periodic response. This system is modeled as a piecewise linear system with discontinuity in the net restoring force, caused by additional damping in the contact-zone. The periodic orbits are classified by their number of subspace boundary crossings and Floquet multipliers. For this classification, the known analytical solutions in the different subspaces are used in the multiple shooting algorithm and a continuation method. Some observations are also presented about the qualitative features (such as symmetry, rigid body solutions) exhibited by this class of systems.

Originele taal-2	English
Titel	Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA
Pagina's	173-182
Aantal pagina's	10
Volume	5
ISBN van elektronische versie	0-7918-3806-4
DOI's	https://doi.org/10.1115/DETC2007-34236
Status	Published - 2008
Extern gepubliceerd	Ja
Evenement	6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C - Las Vegas, United States Duur: 4-sep-2007 → 7-sep-2007

Conference

Conference	6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
Land/Regio	United States
Stad	Las Vegas
Periode	04/09/2007 → 07/09/2007

Toegang tot document

10.1115/DETC2007-34236

Citeer dit

Besselink, B., Shukla, A., Fey, R., & Nijmeijer, H. (2008). Classification of periodic solutions in a single-degree-of-freedom system with backlash. In Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA (Vol. 5, blz. 173-182) https://doi.org/10.1115/DETC2007-34236

Besselink, Bart ; Shukla, Amit ; Fey, Rob ; Nijmeijer, Henk. / Classification of periodic solutions in a single-degree-of-freedom system with backlash. Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA. Vol. 5 2008. blz. 173-182

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title = "Classification of periodic solutions in a single-degree-of-freedom system with backlash",

abstract = "In this paper a single degree-of-freedom system with backlash is studied for its periodic response. This system is modeled as a piecewise linear system with discontinuity in the net restoring force, caused by additional damping in the contact-zone. The periodic orbits are classified by their number of subspace boundary crossings and Floquet multipliers. For this classification, the known analytical solutions in the different subspaces are used in the multiple shooting algorithm and a continuation method. Some observations are also presented about the qualitative features (such as symmetry, rigid body solutions) exhibited by this class of systems.",

author = "Bart Besselink and Amit Shukla and Rob Fey and Henk Nijmeijer",

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booktitle = "Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA",

note = "6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ; Conference date: 04-09-2007 Through 07-09-2007",

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Besselink, B, Shukla, A, Fey, R & Nijmeijer, H 2008, Classification of periodic solutions in a single-degree-of-freedom system with backlash. in Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA. vol. 5, blz. 173-182, 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, Nevada, United States, 04/09/2007. https://doi.org/10.1115/DETC2007-34236

Classification of periodic solutions in a single-degree-of-freedom system with backlash. / Besselink, Bart; Shukla, Amit; Fey, Rob; Nijmeijer, Henk.

Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA. Vol. 5 2008. blz. 173-182.

Onderzoeksoutput › Academic › peer review

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T1 - Classification of periodic solutions in a single-degree-of-freedom system with backlash

AU - Besselink, Bart

AU - Shukla, Amit

AU - Fey, Rob

AU - Nijmeijer, Henk

PY - 2008

Y1 - 2008

N2 - In this paper a single degree-of-freedom system with backlash is studied for its periodic response. This system is modeled as a piecewise linear system with discontinuity in the net restoring force, caused by additional damping in the contact-zone. The periodic orbits are classified by their number of subspace boundary crossings and Floquet multipliers. For this classification, the known analytical solutions in the different subspaces are used in the multiple shooting algorithm and a continuation method. Some observations are also presented about the qualitative features (such as symmetry, rigid body solutions) exhibited by this class of systems.

AB - In this paper a single degree-of-freedom system with backlash is studied for its periodic response. This system is modeled as a piecewise linear system with discontinuity in the net restoring force, caused by additional damping in the contact-zone. The periodic orbits are classified by their number of subspace boundary crossings and Floquet multipliers. For this classification, the known analytical solutions in the different subspaces are used in the multiple shooting algorithm and a continuation method. Some observations are also presented about the qualitative features (such as symmetry, rigid body solutions) exhibited by this class of systems.

U2 - 10.1115/DETC2007-34236

DO - 10.1115/DETC2007-34236

M3 - Conference contribution

SN - 0-7918-4806-X

VL - 5

SP - 173

EP - 182

BT - Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA

T2 - 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C

Y2 - 4 September 2007 through 7 September 2007

ER -

Besselink B, Shukla A, Fey R, Nijmeijer H. Classification of periodic solutions in a single-degree-of-freedom system with backlash. In Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, Las Vegas, USA. Vol. 5. 2008. blz. 173-182 https://doi.org/10.1115/DETC2007-34236