Intrinsic localized modes in micro-scale oscillator arrays subjected to deterministic excitation and white noise

Subramanian Ramakrishnan, Balakumar Balachandran

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

5 Citations (Scopus)

Abstract

The authors study the influence of noise on an array of micro-scale oscillators with a focus on the phenomenon of intrinsic localized modes (ILMs). It is shown numerically that a white noise excitation, by itself, is unable to produce ILMs. However, under a combined deterministic and random excitation, a noise strength threshold is observed beyond which the ILM at one location in attenuated whilst the localization at another location is strengthened. The results motivate an analytical approach wherein the Fokker-Planck equation and approximate moment evolution equations are derived for a typical cell of the array. Numerical solutions of the moment equations suggest that once a localization event occurs in the array, an excitation with noise strength above a threshold value contributes to the persistence of the event. The reported results can form the basis for developing a fundamental understanding of the influence of noise on ILMs in coupled arrays of nonlinear oscillators including micro-scale oscillator arrays.

Original languageEnglish (US)
Title of host publicationIUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems
Pages325-334
Number of pages10
Volume19
DOIs
StatePublished - Dec 1 2010
EventIUTAM Symposium on Multi-Functional Material Structures and Systems - Benguluru, India
Duration: Dec 10 2008Dec 12 2008

Publication series

NameIUTAM Bookseries
Volume19
ISSN (Print)1875-3507

Other

OtherIUTAM Symposium on Multi-Functional Material Structures and Systems
CountryIndia
CityBenguluru
Period12/10/0812/12/08

Fingerprint

White noise
white noise
oscillators
Fokker Planck equation
excitation
moments
thresholds
Fokker-Planck equation
cells

Keywords

  • Intrinsic localized modes
  • Micro-scale oscillators
  • Nonlinear vibration
  • White noise

Cite this

Ramakrishnan, S., & Balachandran, B. (2010). Intrinsic localized modes in micro-scale oscillator arrays subjected to deterministic excitation and white noise. In IUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems (Vol. 19, pp. 325-334). (IUTAM Bookseries; Vol. 19). https://doi.org/10.1007/978-90-481-3771-8-33

Intrinsic localized modes in micro-scale oscillator arrays subjected to deterministic excitation and white noise. / Ramakrishnan, Subramanian; Balachandran, Balakumar.

IUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems. Vol. 19 2010. p. 325-334 (IUTAM Bookseries; Vol. 19).

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

Ramakrishnan, S & Balachandran, B 2010, Intrinsic localized modes in micro-scale oscillator arrays subjected to deterministic excitation and white noise. in IUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems. vol. 19, IUTAM Bookseries, vol. 19, pp. 325-334, IUTAM Symposium on Multi-Functional Material Structures and Systems, Benguluru, India, 12/10/08. https://doi.org/10.1007/978-90-481-3771-8-33
Ramakrishnan S, Balachandran B. Intrinsic localized modes in micro-scale oscillator arrays subjected to deterministic excitation and white noise. In IUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems. Vol. 19. 2010. p. 325-334. (IUTAM Bookseries). https://doi.org/10.1007/978-90-481-3771-8-33
Ramakrishnan, Subramanian ; Balachandran, Balakumar. / Intrinsic localized modes in micro-scale oscillator arrays subjected to deterministic excitation and white noise. IUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems. Vol. 19 2010. pp. 325-334 (IUTAM Bookseries).
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