Nonlinear vibration behavior of graphene resonators and their applications in sensitive mass detection

Abstract

Graphene has received significant attention due to its excellent mechanical properties, which has resulted in the emergence of graphene-based nano-electro-mechanical system such as nanoresonators. The nonlinear vibration of a graphene resonator and its application to mass sensing (based on nonlinear oscillation) have been poorly studied, although a graphene resonator is able to easily reach the nonlinear vibration. In this work, we have studied the nonlinear vibration of a graphene resonator driven by a geometric nonlinear effect due to an edge-clamped boundary condition using a continuum elastic model such as a plate model. We have shown that an in-plane tension can play a role in modulating the nonlinearity of a resonance for a graphene. It has been found that the detection sensitivity of a graphene resonator can be improved by using nonlinear vibration induced by an actuation force-driven geometric nonlinear effect. It is also shown that an in-plane tension can control the detection sensitivity of a graphene resonator that operates both harmonic and nonlinear oscillation regimes. Our study suggests the design principles of a graphene resonator as a mass sensor for developing a novel detection scheme using graphene-based nonlinear oscillators.

Detecting the mass and position of an adsorbate on a drum resonator

“…Because only the axisymmetric modes are used, the position detected by the method is the radial position. Equation (2.13) is for an undamped system, which has also been used to model many CNT and graphene resonators [14,16,30,31,42]. In reality, because the membrane energy dissipates, damping exists.…”

“…In a forward problem, the adsorbate mass and position are given to calculate the resonant frequency [30][31][32][33][34]. However, in the real application of a mass resonator, resonant frequencies are the measured quantities; the adsorbate mass and position are the unknowns to be determined [35].…”

Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

“…The potential applications of graphene are everywhere [16]. Nanoscale engineering devices that use graphene as a material for basic components in resonators, switches, and valves are being developed in many industries [1,4,5,12,13,23,24]. Understanding the mechanical responses of graphene structure elements subject to applied loads are clearly important, see e.g., [15], and above mentioned references.…”

“…Understanding the mechanical responses of graphene structure elements subject to applied loads are clearly important, see e.g., [15], and above mentioned references. The use of graphene as an actuating cantilever beam subject to electric pull-in force can be a major improvement over the use of the traditional pull-in materials, since graphene is more durable, stronger, and corrosion resistant, see e.g., [1,4,12,13]. Many researchers have been using the linear constitutive equation in their models for graphene devices, see [1,4,19,23].…”

“…The use of graphene as an actuating cantilever beam subject to electric pull-in force can be a major improvement over the use of the traditional pull-in materials, since graphene is more durable, stronger, and corrosion resistant, see e.g., [1,4,12,13]. Many researchers have been using the linear constitutive equation in their models for graphene devices, see [1,4,19,23]. For example, a headphone equipped with a graphene membrane has become a real life application of graphene [16,23], however the mathematical model for the membrane reported in the work [23] considered graphene as a linear elastic material and a linear lumped parameter model based on Hooke's law was used to estimate the frequencies of vibrations.…”