Mechanical vibrations of carbon nanotube-based mass sensors: an analytical approach

Abstract

Purpose – The purpose of this paper is to examine the potential of single-walled carbon nanotubes as mass sensors by developing analytical expressions and then comparing the outcome with structural mechanics corresponding predictions. Design/methodology/approach – The carbon nanotube (CNT) resonators are assumed to be either single or double clamped. Analytical formulas capable of describing the vibrational behavior of such CNT-based nanoresonators with an attached mass at nanotube tip or various intermediate positions are developed by combining the Euler–Bernoulli theory and Krylov–Duncan functions. Findings – The validity and the accuracy of these formulas are examined for a wide range of cases via comparisons with corresponding results arisen by spring- or beam-based structural mechanics predictions. Both structural mechanics approaches utilize three-dimensional nanoscale elements formulated according to the molecular theory. The results indicate that the new sensor equations may be utilized for the estimation of vibration response of CNT-based mass sensors with reasonable accuracy. Originality/value – Simple analytical formulas are proved to approximate the mass sensing ability of CNTs adequately, the fact that may significantly contribute in the effort of developing new sensor devices.