A Theoretical Examination of Carbon Nanotubes as a Nano Jump Rope

William Conley, Purdue University

Carbon nanotubes (CNTs) were published in 1991 by Iijima. Since then many different devices have been designed which utilize these unique carbon structures. This work focuses on a CNT which oscillates over a trench, in a configuration similar to an electric wire suspended between two poles. Forcing is applied via the capacitance between a CNT and a conducting plane. The small mechanical oscillations result in the electrical resistance of the CNT varying through the periodic motion. The CNT is of theoretical interest due to its very large Young’s modulus and very small radius of gyration (measuring the hollow-ness of the cross section). The governing PDE is first derived using continuum beam mechanics. Nonlinear beam models produce a cubic nonlinearity coupling the two transverse directions of vibration. A theoretical study using analytical techniques is performed to determine the regions where a whirling instability may occur. This whirling instability corresponds to a pitchfork bifurcation in the equations derived using the method of averaging. A whirling instability results a jump rope like motion of the CNT. These nonlinearities result in sharp transitions between different motions having applications for sensors and circuit elements.

Abstract Author(s): W.G. Conley, C.M. Krousgrill, A. Raman