Bifurcation dynamics of a perturbed intrinsic localized mode in a driven micromechanical array

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  • Sato M.
    School of Natural Science and Technology, Kanazawa University
  • Takao Y.
    School of Natural Science and Technology, Kanazawa University
  • Sada Y.
    School of Natural Science and Technology, Kanazawa University
  • Shi W.
    School of Natural Science and Technology, Kanazawa University
  • Shige S.
    School of Natural Science and Technology, Kanazawa University
  • Sievers A. J.
    Laboratory of Atomic and Solid State Physics, Cornell University

Abstract

The experimental linear response spectrum of an auto-resonant intrinsic localized mode (ILM) in a driven 1-D cantilever array is composed of several resonances including a phase mode of the ILM. This autoresonant state is stable in a finite frequency range between the upper and lower bifurcation frequencies. Here we examine the robustness of the lower frequency transition point to an added lattice perturbation. In the unperturbed ILM state an even linear localized mode crosses the phase mode as the transition is approached and bifurcation occurs when the phase mode intersects the highest-frequency odd-symmetry band mode of the lattice. When an impurity mode is introduced into the lattice near the even linear local mode it breaks the local symmetry so that the lower bifurcation frequency of the ILM is now shifted to the point where the even mode and the odd phase mode frequencies coalesce.

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