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

Library availability

Discover UIUC Full Text

Cite this

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 [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

@inproceedings{d12c9cb6d765404f87884cfde086646f,

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

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.",

author = "Georgiou, {Ioannis T.} and Vakakis, {Alexander F.}",

note = "Publisher Copyright: {\textcopyright} 1997 by ASME.; ASME 1997 Design Engineering Technical Conferences, DETC 1997 ; Conference date: 14-09-1997 Through 17-09-1997",

year = "1997",

doi = "10.1115/DETC97/VIB-3954",

language = "English (US)",

series = "Proceedings of the ASME Design Engineering Technical Conference",

publisher = "American Society of Mechanical Engineers (ASME)",

booktitle = "16th Biennial Conference on Mechanical Vibration and Noise",

}

TY - GEN

T1 - Invariant nnm manifolds for studying localized and chaotic dynamics of an array composed of stiff/soft elements

AU - Georgiou, Ioannis T.

AU - Vakakis, Alexander F.

PY - 1997

Y1 - 1997

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85101973668&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85101973668&partnerID=8YFLogxK

U2 - 10.1115/DETC97/VIB-3954

DO - 10.1115/DETC97/VIB-3954

M3 - Conference contribution

AN - SCOPUS:85101973668

T3 - Proceedings of the ASME Design Engineering Technical Conference

BT - 16th Biennial Conference on Mechanical Vibration and Noise

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME 1997 Design Engineering Technical Conferences, DETC 1997

Y2 - 14 September 1997 through 17 September 1997

ER -

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

Abstract

Publication series

Conference

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this