The high dimensional harmonic balance analysis for second-order delay-differential equations

Liping Liu; Tamás Kalmár-Nagy; Earl H. Dowell

doi:10.1115/detc2007-34396

The high dimensional harmonic balance analysis for second-order delay-differential equations

Liping Liu
, Tamás Kalmár-Nagy
, Earl H. Dowell

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper we demonstrate the utility of the High Dimensional Harmonic Balance (HDHB) method to compute periodic orbits of second-order delay-differential equations. In particular, the method has been successfully applied to capture the unstable limit cycles of a model of regenerative machine tool vibrations. Both the conventional harmonic balance and the HDHB methods are employed to investigate the dynamic behavior of the nonlinear delay equation. The results show an excellent agreement with those from time domain solutions. The advantages of HDHB over the classical Harmonic Balance method are highlighted and discussed. Copyright © 2007 by ASME.

Original language	English
Title of host publication	6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
Volume	5
DOIs	https://doi.org/10.1115/detc2007-34396
State	Published - 2008

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10.1115/detc2007-34396

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Liu, L., Kalmár-Nagy, T., & Dowell, E. H. (2008). The high dimensional harmonic balance analysis for second-order delay-differential equations. In 6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 (Vol. 5) https://doi.org/10.1115/detc2007-34396

Liu, Liping ; Kalmár-Nagy, Tamás ; Dowell, Earl H. / The high dimensional harmonic balance analysis for second-order delay-differential equations. 6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007. Vol. 5 2008.

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title = "The high dimensional harmonic balance analysis for second-order delay-differential equations",

abstract = "In this paper we demonstrate the utility of the High Dimensional Harmonic Balance (HDHB) method to compute periodic orbits of second-order delay-differential equations. In particular, the method has been successfully applied to capture the unstable limit cycles of a model of regenerative machine tool vibrations. Both the conventional harmonic balance and the HDHB methods are employed to investigate the dynamic behavior of the nonlinear delay equation. The results show an excellent agreement with those from time domain solutions. The advantages of HDHB over the classical Harmonic Balance method are highlighted and discussed. Copyright {\textcopyright} 2007 by ASME.",

author = "Liping Liu and Tam{\'a}s Kalm{\'a}r-Nagy and Dowell, \{Earl H.\}",

year = "2008",

doi = "10.1115/detc2007-34396",

language = "English",

volume = "5",

booktitle = "6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007",

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Liu, L, Kalmár-Nagy, T & Dowell, EH 2008, The high dimensional harmonic balance analysis for second-order delay-differential equations. in 6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007. vol. 5. https://doi.org/10.1115/detc2007-34396

The high dimensional harmonic balance analysis for second-order delay-differential equations. / Liu, Liping; Kalmár-Nagy, Tamás; Dowell, Earl H.
6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007. Vol. 5 2008.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The high dimensional harmonic balance analysis for second-order delay-differential equations

AU - Liu, Liping

AU - Kalmár-Nagy, Tamás

AU - Dowell, Earl H.

PY - 2008

Y1 - 2008

N2 - In this paper we demonstrate the utility of the High Dimensional Harmonic Balance (HDHB) method to compute periodic orbits of second-order delay-differential equations. In particular, the method has been successfully applied to capture the unstable limit cycles of a model of regenerative machine tool vibrations. Both the conventional harmonic balance and the HDHB methods are employed to investigate the dynamic behavior of the nonlinear delay equation. The results show an excellent agreement with those from time domain solutions. The advantages of HDHB over the classical Harmonic Balance method are highlighted and discussed. Copyright © 2007 by ASME.

AB - In this paper we demonstrate the utility of the High Dimensional Harmonic Balance (HDHB) method to compute periodic orbits of second-order delay-differential equations. In particular, the method has been successfully applied to capture the unstable limit cycles of a model of regenerative machine tool vibrations. Both the conventional harmonic balance and the HDHB methods are employed to investigate the dynamic behavior of the nonlinear delay equation. The results show an excellent agreement with those from time domain solutions. The advantages of HDHB over the classical Harmonic Balance method are highlighted and discussed. Copyright © 2007 by ASME.

UR - https://dx.doi.org/10.1115/DETC2007-34396

U2 - 10.1115/detc2007-34396

DO - 10.1115/detc2007-34396

M3 - Conference contribution

VL - 5

BT - 6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007

ER -

Liu L, Kalmár-Nagy T, Dowell EH. The high dimensional harmonic balance analysis for second-order delay-differential equations. In 6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007. Vol. 5. 2008 doi: 10.1115/detc2007-34396

The high dimensional harmonic balance analysis for second-order delay-differential equations

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