resonance capture; passive energy transfer; essential nonlinearity; nonlinear energy sinks; energy pumping
Abstract :
[en] We study numerically and analytically the dynamics of passive energy transfer from a damped linear oscillator to an essentially nonlinear end attachment. This transfer is caused by either fundamental or subharmonic resonance capture, and in some cases is initiated by nonlinear beat phenomena. It is shown that, due to the essential nonlinearity, the end attachment is capable of passively absorbing broadband energy at both high and low frequencies, acting, in essence, as a passive broadband boundary controller. Complicated transitions in the damped dynamics can be interpreted based on the topological structure and bifurcations of the periodic solutions of the underlying undamped system. Moreover, complex resonance capture cascades are numerically encountered when we increase the number of degrees of freedom of the system. The ungrounded essentially nonlinear end attachment discussed in this work can find application in numerous practical settings, including vibration and shock isolation of structures, seismic isolation,. utter suppression, and packaging.
Disciplines :
Mechanical engineering Physics Mathematics
Author, co-author :
Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Lee, Young Sup; University of Illinois > Department of Mechanical and Industrial Engineering
Vakakis, Alexander F.; National Technical University of Athens - NTUA > Department of Applied Mathematical and Physical Sciences
McFarland, D. Michael; University of Illinois > Department of Aerospace Engineering
Bergman, Lawrence A.; University of Illinois > Department of Aerospace Engineering
Language :
English
Title :
Irreversible passive energy transfer in coupled oscillators with essential nonlinearity
Publication date :
2006
Journal title :
SIAM Journal on Applied Mathematics
ISSN :
0036-1399
eISSN :
1095-712X
Publisher :
Siam Publications, Philadelphia, United States - Pennsylvania
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