Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays

Subramanian Ramakrishnan, Balakumar Balachandran

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Discrete Breathers, which are dynamical localizations of energy observed in the response of periodic, discrete Hamiltonian lattices to external forcing, have been recently observed in the response of micro-scale cantilever arrays. In this article, the authors invoke an analytical formalism introduced in their previous work to study the influence of white noise excitation on the formation and destruction of discrete breathers in a micro-scale cantilever array with strong intersite nonlinearities. The Fokker-Planck equation for a typical element of the array is derived. Numerical solutions to a system of approximate moment evolution equations obtained from the Fokker-Planck equation elucidate the influence of noise of varying intensity on the emergence and sustenance of discrete breathers in the array. The reported results can form the basis for developing a fundamental understanding of the influence of noise on breathers in coupled arrays of nonlinear oscillators with strong intersite nonlinearities including arrays of microelectromechanical systems.

Original languageEnglish (US)
Title of host publicationIUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments
PublisherSpringer Verlag
Pages247-254
Number of pages8
Volume30
ISBN (Print)9789400716421
DOIs
StatePublished - 2011
EventIUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, 2010 - Budapest, Hungary
Duration: Jun 7 2010Jun 11 2010

Publication series

NameSolid Mechanics and its Applications
Volume30
ISSN (Print)1875-3507

Other

OtherIUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, 2010
CountryHungary
CityBudapest
Period6/7/106/11/10

Fingerprint

Fokker Planck equation
Hamiltonians
White noise
MEMS

Cite this

Ramakrishnan, S., & Balachandran, B. (2011). Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays. In IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments (Vol. 30, pp. 247-254). (Solid Mechanics and its Applications; Vol. 30). Springer Verlag. https://doi.org/10.1007/978-94-007-1643-8_28

Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays. / Ramakrishnan, Subramanian; Balachandran, Balakumar.

IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. Vol. 30 Springer Verlag, 2011. p. 247-254 (Solid Mechanics and its Applications; Vol. 30).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ramakrishnan, S & Balachandran, B 2011, Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays. in IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. vol. 30, Solid Mechanics and its Applications, vol. 30, Springer Verlag, pp. 247-254, IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, 2010, Budapest, Hungary, 6/7/10. https://doi.org/10.1007/978-94-007-1643-8_28
Ramakrishnan S, Balachandran B. Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays. In IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. Vol. 30. Springer Verlag. 2011. p. 247-254. (Solid Mechanics and its Applications). https://doi.org/10.1007/978-94-007-1643-8_28
Ramakrishnan, Subramanian ; Balachandran, Balakumar. / Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays. IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. Vol. 30 Springer Verlag, 2011. pp. 247-254 (Solid Mechanics and its Applications).
@inproceedings{5e084b0c7eb04e4495dd4e0a1558aafa,
title = "Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays",
abstract = "Discrete Breathers, which are dynamical localizations of energy observed in the response of periodic, discrete Hamiltonian lattices to external forcing, have been recently observed in the response of micro-scale cantilever arrays. In this article, the authors invoke an analytical formalism introduced in their previous work to study the influence of white noise excitation on the formation and destruction of discrete breathers in a micro-scale cantilever array with strong intersite nonlinearities. The Fokker-Planck equation for a typical element of the array is derived. Numerical solutions to a system of approximate moment evolution equations obtained from the Fokker-Planck equation elucidate the influence of noise of varying intensity on the emergence and sustenance of discrete breathers in the array. The reported results can form the basis for developing a fundamental understanding of the influence of noise on breathers in coupled arrays of nonlinear oscillators with strong intersite nonlinearities including arrays of microelectromechanical systems.",
author = "Subramanian Ramakrishnan and Balakumar Balachandran",
year = "2011",
doi = "10.1007/978-94-007-1643-8_28",
language = "English (US)",
isbn = "9789400716421",
volume = "30",
series = "Solid Mechanics and its Applications",
publisher = "Springer Verlag",
pages = "247--254",
booktitle = "IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments",

}

TY - GEN

T1 - Influence of noise on discrete breathers in nonlinearly coupled micro-oscillator arrays

AU - Ramakrishnan, Subramanian

AU - Balachandran, Balakumar

PY - 2011

Y1 - 2011

N2 - Discrete Breathers, which are dynamical localizations of energy observed in the response of periodic, discrete Hamiltonian lattices to external forcing, have been recently observed in the response of micro-scale cantilever arrays. In this article, the authors invoke an analytical formalism introduced in their previous work to study the influence of white noise excitation on the formation and destruction of discrete breathers in a micro-scale cantilever array with strong intersite nonlinearities. The Fokker-Planck equation for a typical element of the array is derived. Numerical solutions to a system of approximate moment evolution equations obtained from the Fokker-Planck equation elucidate the influence of noise of varying intensity on the emergence and sustenance of discrete breathers in the array. The reported results can form the basis for developing a fundamental understanding of the influence of noise on breathers in coupled arrays of nonlinear oscillators with strong intersite nonlinearities including arrays of microelectromechanical systems.

AB - Discrete Breathers, which are dynamical localizations of energy observed in the response of periodic, discrete Hamiltonian lattices to external forcing, have been recently observed in the response of micro-scale cantilever arrays. In this article, the authors invoke an analytical formalism introduced in their previous work to study the influence of white noise excitation on the formation and destruction of discrete breathers in a micro-scale cantilever array with strong intersite nonlinearities. The Fokker-Planck equation for a typical element of the array is derived. Numerical solutions to a system of approximate moment evolution equations obtained from the Fokker-Planck equation elucidate the influence of noise of varying intensity on the emergence and sustenance of discrete breathers in the array. The reported results can form the basis for developing a fundamental understanding of the influence of noise on breathers in coupled arrays of nonlinear oscillators with strong intersite nonlinearities including arrays of microelectromechanical systems.

UR - http://www.scopus.com/inward/record.url?scp=85032656867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032656867&partnerID=8YFLogxK

U2 - 10.1007/978-94-007-1643-8_28

DO - 10.1007/978-94-007-1643-8_28

M3 - Conference contribution

SN - 9789400716421

VL - 30

T3 - Solid Mechanics and its Applications

SP - 247

EP - 254

BT - IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments - Proceedings of the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments

PB - Springer Verlag

ER -