Nonlinear vibration modes in micro-resonator arrays

Nonlinear phenomena such as mode localization have been studied for a number of years in the solid-state physics literature. Energy can become localized at a specific location in a discrete system as a result of the nonlinearity of the system and not due to any defects or impurities within the considered systems. Intrinsic Localized Modes (ILMs), which are defined as localization due to strong intrinsic nonlinearity within an array of perfect, periodically repeating oscillators, are of interest to the present work. Here, such localization is studied in the context of micro-cantilever arrays and micro-resonator arrays, and it is explored if an ILM can be realized as a nonlinear normal mode or nonlinear vibration mode. The method of multiple scales and methods to determine nonlinear normal modes are used to study the nonlinear vibrations of the resonator arrays. Preliminary investigations reported in this article suggest that it is possible to realize an ILM as a nonlinear vibration mode. These results are believed to be important for future designs of microresonator arrays intended for signal processing, communication, and sensor applications.

[1]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

[2]  Willis,et al.  Discreteness effects on the formation and propagation of breathers in nonlinear Klein-Gordon equations. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  A. V. Ustinov.  Imaging of discrete breathers. , 2003, Chaos.

[4]  Balakumar Balachandran,et al.  Parametric identification of piezoelectric microscale resonators , 2006 .

[5]  B. Balachandran,et al.  NONLINEAR PHENOMENA IN MICROELECTROMECHANICAL RESONATORS , 2005 .

[6]  Yuri S. Kivshar,et al.  Localizing Energy Through Nonlinearity and Discreteness , 2004 .

[7]  Demetrios N. Christodoulides,et al.  Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices , 2003, Nature.

[8]  L Q English,et al.  Study of intrinsic localized vibrational modes in micromechanical oscillator arrays. , 2003, Chaos.

[9]  P. Marko,et al.  ABSENCE OF DIFFUSION IN CERTAIN RANDOM LATTICES , 2008 .

[10]  Choi Hui Pak.  Nonlinear Normal Mode Dynamics , 1997 .

[11]  B. Hubbard,et al.  Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array. , 2003, Physical review letters.

[12]  A. J. Sievers,et al.  Optical manipulation of intrinsic localized vibrational energy in cantilever arrays , 2004, nlin/0403031.

[13]  Yu. A. Kuznetsov,et al.  Applied nonlinear dynamics: Analytical, computational, and experimental methods , 1996 .

[14]  Vimal Singh,et al.  Perturbation methods , 1991 .

[15]  B. Balachandran,et al.  Intrinsic Localized Modes and Nonlinear Normal Modes in Micro-Resonator Arrays , 2005 .

[16]  Ali H. Nayfeh,et al.  Nonlinear Interactions: Analytical, Computational, and Experimental Methods , 2000 .

[17]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .