Nonlinear Dynamic Response of Cantilevered Carbon Nanotube Resonator by Electrostatic Excitation

Abstract

This paper predicted nonlinear dynamic responses of a cantilevered carbon nanotube(CNT) resonator incorporating the electrostatic forces and van der Waals interactions between the CNT cantilever and ground plane. The structural model of CNT includes geometric and inertial nonlinearities to investigate various phenomena of nonlinear responses of the CNT due to the electrostatic excitation.In order to solve this problem, we used Galerkin's approximation and the numerical integration techniques. As a result, the CNT nano-resonator shows the softening effect through saddle-node bifurcation near primary resonance frequency with increasing the applied AC and DC voltages. Also we can predict nonlinear secondary resonances such as superharmonic and subharmonic resonances.The superharmonic resonance of the nano-resonator is influenced by applied AC voltage. The period-doubling bifurcation leads to the subharmonic resonance which occurs when the nano-resonator is actuated by electrostatic forces as parametric excitation. 는 선형보로 가정한 CNT의 구형파 전압가진

Theoretical investigation of nonlinear resonances in a carbon nanotube cantilever with a tip-mass under electrostatic excitation

“…5(a)), the nano-resonator exhibited a very weak superharmonic resonance peak and no phase difference at half the fundamental harmonic frequency because of the low ratio of AC voltage between DC and AC harmonic excitation, unlike in our previous work. 4 However, the primary resonance peak occurred at the fundamental frequency with a phase difference of p. Figures 5(b) and 5(c) show that the nano-resonator softened and the SN bifurcation occurred at the fundamental resonance branch under higher DC voltage. At increasing excitation voltages, the natural frequency decreased, 24 but the unstable region increased.…”

“…For an increasing tip mass ratio, the resonance branch softened more than the case of only geometric nonlinearity. The softening effects 21 branch occurred because the cubic nonlinearity of the equation of motion became strongly negative with increasing applied voltage 4 or inertial nonlinearity. The stiffening effects at the resonance branch were due to the positive cubic term.…”

“…However, except for tip mass effects, the nano-resonator had the PD bifurcation at subharmonic resonance branch only the under conditions of a high electrostatic field. 2,4 In this study, the tip mass effects led to the PD bifurcation of the system. These results show that the PD bifurcation occurred not only under high electrostatic forces but also with a tip mass effect, as illustrated in Fig.…”

“…Conversely, in previous work, 4 we monitored the pull-in behavior when it was difficult to use a resonator driven by a frequency within the escape band. Furthermore, when the Pauli repulsion force was considered, there was an unstable response like bouncing or tapping as the CNT approached the ground plane.…”

“…Nano-devices that take advantage of the low density, high aspect ratio, and high conductivity of a CNT include nano-resonators [1][2][3][4] or mass sensors. [5][6][7] Nano-resonators are based on electromechanical resonance responses of a cantilevered CNT to electrostatic excitation.…”