Invariant nnm manifolds for studying localized and chaotic dynamics of an array composed of stiff/soft elements

Ioannis T. Georgiou; Alexander F. Vakakis

doi:10.1115/DETC97/VIB-3954

Invariant nnm manifolds for studying localized and chaotic dynamics of an array composed of stiff/soft elements

Ioannis T. Georgiou, Alexander F. Vakakis

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This study concerns propagation of waves in a coupled array of soft/sti oscillators. We show that the array supports a fam- ily of purely slow waves, including a solitary one, and a family of purely fast waves. The slow and fast waves interact to give rise to chaotically modulated slow/fast and fast/slow waves. Slow and fast waves are realized as two-dimensional invariant manifolds (normal modes) in phase space of a singular perturbation problem.

Original language	English (US)
Title of host publication	16th Biennial Conference on Mechanical Vibration and Noise
Publisher	American Society of Mechanical Engineers (ASME)
ISBN (Electronic)	9780791880401
DOIs	https://doi.org/10.1115/DETC97/VIB-3954
State	Published - 1997
Event	ASME 1997 Design Engineering Technical Conferences, DETC 1997 - Sacramento, United States Duration: Sep 14 1997 → Sep 17 1997

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	1A-1997

Conference

Conference	ASME 1997 Design Engineering Technical Conferences, DETC 1997
Country/Territory	United States
City	Sacramento
Period	9/14/97 → 9/17/97

ASJC Scopus subject areas

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

Online availability

10.1115/DETC97/VIB-3954

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Georgiou, I. T., & Vakakis, A. F. (1997). Invariant nnm manifolds for studying localized and chaotic dynamics of an array composed of stiff/soft elements. In 16th Biennial Conference on Mechanical Vibration and Noise Article V01AT05A008 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1A-1997). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC97/VIB-3954

Invariant nnm manifolds for studying localized and chaotic dynamics of an array composed of stiff/soft elements. / Georgiou, Ioannis T.; Vakakis, Alexander F.
16th Biennial Conference on Mechanical Vibration and Noise. American Society of Mechanical Engineers (ASME), 1997. V01AT05A008 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1A-1997).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Georgiou, IT & Vakakis, AF 1997, Invariant nnm manifolds for studying localized and chaotic dynamics of an array composed of stiff/soft elements. in 16th Biennial Conference on Mechanical Vibration and Noise., V01AT05A008, Proceedings of the ASME Design Engineering Technical Conference, vol. 1A-1997, American Society of Mechanical Engineers (ASME), ASME 1997 Design Engineering Technical Conferences, DETC 1997, Sacramento, United States, 9/14/97. https://doi.org/10.1115/DETC97/VIB-3954

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AB - This study concerns propagation of waves in a coupled array of soft/sti oscillators. We show that the array supports a fam- ily of purely slow waves, including a solitary one, and a family of purely fast waves. The slow and fast waves interact to give rise to chaotically modulated slow/fast and fast/slow waves. Slow and fast waves are realized as two-dimensional invariant manifolds (normal modes) in phase space of a singular perturbation problem.

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Invariant nnm manifolds for studying localized and chaotic dynamics of an array composed of stiff/soft elements

Abstract

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