Student Thesis Seminar
"Response of Many Nonlinear Driven Oscillators"
Yaron Bromberg
Dept.
of Condensed Matter Physics, Tel Aviv University
We are studying the dynamics of large arrays of coupled nonlinear nanomechanical oscillators.
Our study is motivated by a recent experiment by Eyal Buks and Michael Roukes [1] involving a
parametrically-excited nanomechanical resonator array. Previous analytical calculations using
secular perturbation theory [2] were limited to small arrays of a few resonators. Here we
extend the analytical treatment to large discrete systems and find that the parametric
instability of these systems exhibits nontrivial behavior which takes on a different form
than in other well-known nonlinear systems (e.g. Rayleigh-Benard convection). In particular,
we show that different modes of the system undergo different types of bifurcation, and discuss
the possible experimental consequences of this behavior.
[1] E. Buks and M.L. Roukes, J. MEMS 11, 802 (2002).
[2] R. Lifshitz and M.C. Cross, Phys. Rev. B 67, 134302 (2003).
Thesis Adviser:
Dr. Ron Lifshitz, x5145
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