Three-dimensional energy channeling in the unit-cell model coupled to a spherical rotator II: unidirectional energy channeling

Three-dimensional energy channeling in the unit-cell model coupled to a spherical rotator II:... This work is the second one in a two-part series devoted to the analysis of complex nonlinear mechanism of energy channeling emerging in a locally resonant three-dimensional, unit-cell model, and the current paper considers unidirectional energy channeling. The considered system comprises an external mass subjected to a symmetric three-dimensional linear local potential with an internal spherical rotator. The present study specifically focuses on the analysis of three-dimensional, dissipative mechanism of irreversible (unidirectional) energy transport across mutually orthogonal directions realized in the limit of low-energy excitations. In particular, this study unveils the special transient regimes of three-dimensional partial and complete transformation of in-plane vibrations of the external element to out-of-plane vibrations. Similar to the results reported in the first part of the series, this three-dimensional energy flow is fully governed by the motion of the internal spherical rotator coupled to the external mass. Analysis of this peculiar response regime is based on regular multi-scale asymptotic analysis resulting in a reduced order dissipative slow-flow model. Results of the analysis are substantiated by the numerical simulations of the full model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Three-dimensional energy channeling in the unit-cell model coupled to a spherical rotator II: unidirectional energy channeling

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media Dordrecht
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3587-x
Publisher site
See Article on Publisher Site

Abstract

This work is the second one in a two-part series devoted to the analysis of complex nonlinear mechanism of energy channeling emerging in a locally resonant three-dimensional, unit-cell model, and the current paper considers unidirectional energy channeling. The considered system comprises an external mass subjected to a symmetric three-dimensional linear local potential with an internal spherical rotator. The present study specifically focuses on the analysis of three-dimensional, dissipative mechanism of irreversible (unidirectional) energy transport across mutually orthogonal directions realized in the limit of low-energy excitations. In particular, this study unveils the special transient regimes of three-dimensional partial and complete transformation of in-plane vibrations of the external element to out-of-plane vibrations. Similar to the results reported in the first part of the series, this three-dimensional energy flow is fully governed by the motion of the internal spherical rotator coupled to the external mass. Analysis of this peculiar response regime is based on regular multi-scale asymptotic analysis resulting in a reduced order dissipative slow-flow model. Results of the analysis are substantiated by the numerical simulations of the full model.

Journal

Nonlinear DynamicsSpringer Journals

Published: Aug 1, 2017

References

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