Frequency Response of Primary Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation

This paper deals with electrostatically actuated Double Walled Carbon Nanotubes (DWCNT) cantilever resonators. DWCNTs are modeled as Euler-Bernoulli cantilever beams. Electrostatic, damping, and van der Waals, forces act on the outer tube of the DWCNT, while only van der Waals force acts on the inner tube. A soft AC voltage provides the electrostatic actuation. Van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes. The nonlinearities in the system are given by the electrostatic and van der Waals forces. The DWCNT undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS) is employed to investigate the system under soft excitations and/or weak nonlinearities. A modal coordinate transformation, in which only the linear term of the van der Waals force are considered, and the Harmonic Balance Method (HBM), are used to solve the zero-order problem. Then the frequency-amplitude response is found in the case of primary resonance. The expected nonlinear dynamic behavior is important to improve DWCNT resonator sensitivity in the application of mass sensing.