Mass detection by means of the vibrating nanomechanical resonators

Abstract

We present a theoretical analysis of the vibrating resonator in cantilever and bridge configurations operating as ultrasensitive mass sensors. An exact solution of the problem has been obtained. For the small mass ratio, the asymptotic solutions (which relate the frequency shift, mass ratio, and position of the attached particle) have been derived. It has been shown that the mass and position of the attached particle for the cantilever configuration can be unambiguously resolved by the use of three consecutive resonant frequencies. For the bridge configuration, the particle mass can be deduced by using only two measured resonant frequencies.