Bifurcations and Chaos in an Experimental Based Quasi-Continuum Nonlinear Dynamical System for the ‘Clapper’ Nanoresonator

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.