Construction and use of the frequency-energy plot for a system with two essential nonlinearities

Sean A. Hubbard, Alexander F Vakakis, Lawrence Bergman, D. Michael McFarland

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of depicting possible periodic motions of a strongly nonlinear system in the frequency-energy plane. The particular case of a 2-degree-of-freedom, linear primary structure coupled to a 2-DOF, nonlinear attachment is examined in detail. While there exist numerical tools for the semiautomatic computation of such frequency-energy plots (FEPs), the presence of multiple essential (nonlinearizable) nonlinearities in the present system introduces new challenges in their application. Furthermore, the multiple degrees of freedom of the nonlinear subsystem allow the existence of complex nonlinear normal modes localized there but exhibiting more complicated resonances than those previously observed in the study of a single-DOF nonlinear attachment. The FEP generated for a laboratory-scale mechanical system is interpreted to explain the transitions and energy transfers that occur in the simulated transient response of the combined system following broadband shock excitation.

Original languageEnglish (US)
Title of host publicationASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
Pages449-456
Number of pages8
EditionPARTS A AND B
DOIs
StatePublished - Dec 1 2011
EventASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States
Duration: Aug 28 2011Aug 31 2011

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
NumberPARTS A AND B
Volume1

Other

OtherASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
CountryUnited States
CityWashington, DC
Period8/28/118/31/11

Fingerprint

Transient analysis
Energy transfer
Nonlinear systems
Nonlinearity
Energy
Degree of freedom
Periodic Motion
Transient Response
Normal Modes
Energy Transfer
Mechanical Systems
Broadband
Shock
Subsystem
Nonlinear Systems
Excitation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

Cite this

Hubbard, S. A., Vakakis, A. F., Bergman, L., & McFarland, D. M. (2011). Construction and use of the frequency-energy plot for a system with two essential nonlinearities. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 (PARTS A AND B ed., pp. 449-456). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1, No. PARTS A AND B). https://doi.org/10.1115/DETC2011-48576

Construction and use of the frequency-energy plot for a system with two essential nonlinearities. / Hubbard, Sean A.; Vakakis, Alexander F; Bergman, Lawrence; McFarland, D. Michael.

ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011. PARTS A AND B. ed. 2011. p. 449-456 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1, No. PARTS A AND B).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hubbard, SA, Vakakis, AF, Bergman, L & McFarland, DM 2011, Construction and use of the frequency-energy plot for a system with two essential nonlinearities. in ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011. PARTS A AND B edn, Proceedings of the ASME Design Engineering Technical Conference, no. PARTS A AND B, vol. 1, pp. 449-456, ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, United States, 8/28/11. https://doi.org/10.1115/DETC2011-48576
Hubbard SA, Vakakis AF, Bergman L, McFarland DM. Construction and use of the frequency-energy plot for a system with two essential nonlinearities. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011. PARTS A AND B ed. 2011. p. 449-456. (Proceedings of the ASME Design Engineering Technical Conference; PARTS A AND B). https://doi.org/10.1115/DETC2011-48576
Hubbard, Sean A. ; Vakakis, Alexander F ; Bergman, Lawrence ; McFarland, D. Michael. / Construction and use of the frequency-energy plot for a system with two essential nonlinearities. ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011. PARTS A AND B. ed. 2011. pp. 449-456 (Proceedings of the ASME Design Engineering Technical Conference; PARTS A AND B).
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