We study the stiffening and damping effects that local essentially nonlinear attachments can have on the dynamics of a primary linear structure. These local attachments can be designed to act as nonlinear energy sinks (NESs) of shock-induced energy by engaging in isolated resonance captures or resonance capture cascades with structural modes. After the introduction of the NESs, the effective stiffness and damping properties of the structure are characterized through appropriate measures, developed within this work, which are based on the energy contained within the modes of the primary structure. Three types of NESs are introduced in this work, and their effects on the stiffness and damping properties of the linear structure are studied via (local) instantaneous and (global) weighted-averaged effective stiffness and damping measures. Three different applications are considered and show that these attachments can drastically increase the effective damping properties of a two-degrees-of-freedom system and, to a lesser degree, the stiffening properties as well. An interesting finding reported herein is that the essentially nonlinear attachments can introduce significant nonlinear coupling between distinct structural modes, thus paving the way for nonlinear energy redistribution between structural modes. This feature, coupled with the well-established capacity of NESs to passively absorb and locally dissipate shock energy, can be used to create effective passive mitigation designs of structures under impulsive loads.
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February 2012
Research Papers
Effective Stiffening and Damping Enhancement of Structures With Strongly Nonlinear Local Attachments
Themistoklis P. Sapsis,
Themistoklis P. Sapsis
Department of Mechanical Engineering, Massachusetts Institute of Technology
, Cambridge, MA 02139
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D. Dane Quinn,
D. Dane Quinn
Department of Mechanical Engineering,
The University of Akron
, Akron, OH 44325
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Alexander F. Vakakis,
Alexander F. Vakakis
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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Lawrence A. Bergman
Lawrence A. Bergman
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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Themistoklis P. Sapsis
Department of Mechanical Engineering, Massachusetts Institute of Technology
, Cambridge, MA 02139
D. Dane Quinn
Department of Mechanical Engineering,
The University of Akron
, Akron, OH 44325
Alexander F. Vakakis
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
Lawrence A. Bergman
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801 J. Vib. Acoust. Feb 2012, 134(1): 011016 (12 pages)
Published Online: January 9, 2012
Article history
Received:
December 13, 2010
Revised:
July 11, 2011
Online:
January 9, 2012
Published:
January 9, 2012
Citation
Sapsis, T. P., Dane Quinn, D., Vakakis, A. F., and Bergman, L. A. (January 9, 2012). "Effective Stiffening and Damping Enhancement of Structures With Strongly Nonlinear Local Attachments." ASME. J. Vib. Acoust. February 2012; 134(1): 011016. https://doi.org/10.1115/1.4005005
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