TY - GEN
T1 - Construction and use of the frequency-energy plot for a system with two essential nonlinearities
AU - Hubbard, Sean A.
AU - Vakakis, Alexander F.
AU - Bergman, Lawrence A.
AU - McFarland, D. Michael
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
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U2 - 10.1115/DETC2011-48576
DO - 10.1115/DETC2011-48576
M3 - Conference contribution
AN - SCOPUS:84863600658
SN - 9780791854785
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 449
EP - 456
BT - ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
T2 - ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
Y2 - 28 August 2011 through 31 August 2011
ER -