Research Papers

Localization in Microresonator Arrays: Influence of Natural Frequency Tuning

[+] Author and Article Information
Andrew J. Dick1

Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77005andrew.j.dick@rice.edu

Balakumar Balachandran, C. Daniel Mote

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742


Corresponding author.

J. Comput. Nonlinear Dynam 5(1), 011002 (Nov 10, 2009) (11 pages) doi:10.1115/1.4000314 History: Received September 11, 2008; Revised March 18, 2009; Published November 10, 2009; Online November 10, 2009

Intrinsic localized modes are localization events caused by intrinsic nonlinearities within an array of perfectly periodic coupled oscillators. Recent developments in microscale fabrication techniques have allowed for the studies of this phenomenon in micro-electromechanical systems. Studies have also identified a relationship between the spatial profiles of intrinsic localized modes and forced nonlinear vibration modes, as well as a potential sensitivity to fundamental frequency relationships of one-to-one and three-to-one between adjacent oscillators. For the system considered, the one-to-one frequency relationship is determined to provide nonideal conditions for studying intrinsic localized modes. The influence of the three-to-one frequency relationship on the behavior of the intrinsic localized modes is studied with analytical methods and numerical simulations by tuning the fundamental frequencies of the oscillators. While the perfect tuning condition is not determined to produce a unique phenomenon, the number and energy concentration of the localization events are found to increase with the increased frequency ratio, which results in a decrease in the effective coupling stiffness within the array.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Unit cell of microcantilever array

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Figure 2

Excitation frequency profile and example of localization in a microcantilever array

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Figure 3

Dispersion curves for mono-element (dashed) and di-element (solid) arrays. The horizontal axis corresponds to the wave number and the vertical axis corresponds to the frequency (7).

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Figure 4

Dispersion curves for a di-element array with three-to-one frequency relationship

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Figure 5

Plot of minimum (solid) and maximum (dashed) frequencies of the array for a range of frequency ratios

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Figure 6

Representative ILM simulation results for di-element array with three-to-one frequency relationship

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Figure 7

Comparison of the ILM profile for the original parameter values (solid) with the profile for three-to-one frequency relationship (dashed)

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Figure 8

Four roots of the polynomial of the restricted normal mode approach

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Figure 9

Comparison of results from restricted normal mode approach (dashed) with simulation results (solid)

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Figure 10

Comparison of results from modified invariant-manifold approach (dashed) with simulation results (solid)

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Figure 11

Magnitude of Eq. 28




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