NDLI: Energy localization and white noise-induced enhancement of response in a micro-scale oscillator array

Content Provider	Springer Nature Link
Author	Ramakrishnan, S. Balachandran, B.
Copyright Year	2010
Abstract	In this work, the authors seek to develop an analytical framework to understand the influence of noise on an array of micro-scale oscillators with special attention to the phenomenon of intrinsic localized modes (ILMs). It was recently shown by one of the authors and co-workers (Dick et al. in Nonlinear Dyn. 54:13, 2008) that ILMs can be realized as nonlinear vibration modes. Building on this work, it is shown here that white noise excitation, by itself, is unable to produce ILMs in an array of coupled nonlinear oscillators. However, in the case of an array subjected to a combined deterministic and random excitation, the obtained numerical results indicate the existence of a threshold noise strength beyond which the ILM at one location in attenuated whilst the localization in strengthened at another location in the array. The numerical results further motivate the formulation of a general analytical framework wherein the Fokker–Planck equation is derived for a typical coupled oscillator cell of the array subjected to a combined white noise and deterministic excitation. With a set of approximations, the moment evolution equations are derived from the Fokker–Planck equation and they are numerically solved. These solutions indicate that once a localization event occurs in the array, a random excitation with noise strength above a threshold value contributes to the sustenance of the event. It is also observed that an excitation with a higher noise strength results in enhanced response amplitudes for oscillators in the center of the array. The efforts presented in this paper, in addition to providing an analytical framework for developing a fundamental understanding of the influence of white noise on the dynamics of coupled oscillator arrays, suggest that noise may be potentially used to manipulate the formation and persistence of ILMs in such arrays. Furthermore, the occurrence of enhanced response amplitudes due to an excitation with a high noise strength indicates that the framework may also be used to investigate stochastic resonance-type phenomena in coupled arrays of nonlinear oscillators including micro-scale oscillator arrays.
Starting Page	1
Ending Page	16
Page Count	16
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	62
Issue Number	1-2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-03-27
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear vibration White noise Intrinsic localized modes Micro-scale oscillators Automotive Engineering Mechanical Engineering Mechanics Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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