Carbon nanotube-based resonant nanomechanical sensors: A computational investigation of their behavior

This paper utilizes a spring–mass-based finite element formulation for predicting the vibrational behavior of single- and multi-walled carbon nanotubes to investigate their sensing characteristics when a nanoparticle is attached to them. Three-dimensional nanoscale elements directly formulated from molecular theory and corresponding elemental equations were implemented to simulate the dynamic behavior of nanotubes. The atomistic microstructure of nanotubes was used to assemble elemental equations and construct a dynamic equilibrium equation. In this way, the resonant frequency shifts of cantilevered or bridged nanotubes caused by the additions of nanoscale particles to the nanotube tip and at various intermediate positions were explored. Simulation results agree well with numerical data published in literature. The effects of an added mass on the frequency shift of higher-order vibrational modes of nanotubes were investigated, wherein novel behavior was observed because frequency shift takes an almost constant stable value in several basic vibrational mode independent of the location of the added mass on the carbon nanotube. The frequency shifts of single- and multi-walled carbon nanotubes were also compared. As a final point, the effect of heterogeneous boundary conditions on frequency shifts of multi-walled carbon nanotubes was examined.