The high dimensional harmonic balance analysis for second-order delay-differential equations
Publication
, Journal Article
Liu, L; Kalmár-Nagy, T; Dowell, EH
Published in: 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
June 17, 2008
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.
Duke Scholars
Published In
2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
DOI
Publication Date
June 17, 2008
Volume
5 PART A
Start / End Page
695 / 702
Citation
APA
Chicago
ICMJE
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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. 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007, 5 PART A, 695–702. https://doi.org/10.1115/DETC2007-34396
Liu, L., T. Kalmár-Nagy, and E. H. Dowell. “The high dimensional harmonic balance analysis for second-order delay-differential equations.” 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007 5 PART A (June 17, 2008): 695–702. https://doi.org/10.1115/DETC2007-34396.
Liu L, Kalmár-Nagy T, Dowell EH. The high dimensional harmonic balance analysis for second-order delay-differential equations. 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007. 2008 Jun 17;5 PART A:695–702.
Liu, L., et al. “The high dimensional harmonic balance analysis for second-order delay-differential equations.” 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007, vol. 5 PART A, June 2008, pp. 695–702. Scopus, doi:10.1115/DETC2007-34396.
Liu L, Kalmár-Nagy T, Dowell EH. The high dimensional harmonic balance analysis for second-order delay-differential equations. 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007. 2008 Jun 17;5 PART A:695–702.
Published In
2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
DOI
Publication Date
June 17, 2008
Volume
5 PART A
Start / End Page
695 / 702