On Primary Resonance of Electrostatically Actuated Double Walled Carbon Nanotube Cantilever Biosensors

Abstract

This paper investigates electrostatically actuated Double Walled Carbon Nanotubes (DWCNT) cantilever biosensors using the Method of Multiple Scales (MMS) and the Harmonic Balance Method (HBM). Forces acting on the outer tube of the DWCNT are electrostatic, damping, and van der Waals, while only van der Waals acts on the inner tube. The electrostatic actuation is provided by a soft AC voltage. Van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes; herein, for modal coordinate transformation, only the linear term of the van der Waals force will be considered. The nonlinearity of the motion is produced by the electrostatic and van der Waals forces. The DWCNT undergoes nonlinear parametric dynamics. MMS is employed to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude response is found in the case of primary resonance. DWCNTs are modelled after the Euler-Bernoulli cantilever beam. The expected nonlinear dynamic behavior is important to improve DWCNT resonator sensitivity in the application of mass sensing.