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

Subramanian Ramakrishnan; Balakumar Balachandran

doi:10.1007/978-90-481-3771-8_33

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

Subramanian Ramakrishnan, Balakumar Balachandran

Mechanical & Industrial Engineering

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

6 Scopus citations

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 language	English (US)
Title of host publication	IUTAM Symposium on Multi-Functional Material Structures and Systems - Proceedings of the IUTAM Symposium on Multi-Functional Material Structures and Systems
Publisher	Springer Verlag
Pages	325-334
Number of pages	10
ISBN (Print)	9789048137701
DOIs	https://doi.org/10.1007/978-90-481-3771-8_33
State	Published - 2010
Event	IUTAM Symposium on Multi-Functional Material Structures and Systems - Benguluru, India Duration: Dec 10 2008 → Dec 12 2008

Publication series

Name	IUTAM Bookseries
Volume	19
ISSN (Print)	1875-3507

Other

Other	IUTAM Symposium on Multi-Functional Material Structures and Systems
Country/Territory	India
City	Benguluru
Period	12/10/08 → 12/12/08

Bibliographical note

Funding Information:
Partial support received for this work through ARO Grant No. W911NF05100 76 and NSF Grant No. 0826173 are gratefully acknowledged.

Keywords

Intrinsic localized modes
Micro-scale oscillators
Nonlinear vibration
White noise

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10.1007/978-90-481-3771-8_33

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 (pp. 325-334). (IUTAM Bookseries; Vol. 19). Springer Verlag. 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. Springer Verlag, 2010. p. 325-334 (IUTAM Bookseries; Vol. 19).

Research output: Chapter in Book/Report/Conference proceeding › Conference 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. IUTAM Bookseries, vol. 19, Springer Verlag, 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. Springer Verlag. 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. Springer Verlag, 2010. pp. 325-334 (IUTAM Bookseries).

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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.",

keywords = "Intrinsic localized modes, Micro-scale oscillators, Nonlinear vibration, White noise",

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note = "Funding Information: Partial support received for this work through ARO Grant No. W911NF05100 76 and NSF Grant No. 0826173 are gratefully acknowledged.; IUTAM Symposium on Multi-Functional Material Structures and Systems ; Conference date: 10-12-2008 Through 12-12-2008",

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PY - 2010

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N2 - 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.

AB - 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.

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

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