In this paper we formulate and numerically investigate an experimentally based quasi-continuum nonlinear initial-boundary-value problem for the three-field ‘Clapper’ nanoresonator that consistently incorporates the system geometric nonlinearity with nonlinear contributions of both magnetomotive and electrodynamic excitation. The spatio-temporal field equations are then reduced via symmetry and a modal projection to an equivalent quasiperiodically excited, low order, nonlinear dynamical system. The governing parameters of the resulting system are matched with the experimentally measured resonance conditions for small amplitude response. Numerical analysis reveals a complex bifurcation structure of torus doubling culminating with a chaotic strange attractor that exhibits similar features to that previously measured in the ‘Clapper’ experiment.
- Design Engineering Division and Computers and Information in Engineering Division
Bifurcations and Chaos in an Experimental Based Quasi-Continuum Nonlinear Dynamical System for the ‘Clapper’ Nanoresonator
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Gottlieb, O, Gemintern, A, & Blick, RH. "Bifurcations and Chaos in an Experimental Based Quasi-Continuum Nonlinear Dynamical System for the ‘Clapper’ Nanoresonator." Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 3: 19th International Conference on Design Theory and Methodology; 1st International Conference on Micro- and Nanosystems; and 9th International Conference on Advanced Vehicle Tire Technologies, Parts A and B. Las Vegas, Nevada, USA. September 4–7, 2007. pp. 937-943. ASME. https://doi.org/10.1115/DETC2007-35498
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