Mass and position determination of an accreted particle from the vibration of a beam-based nanomechanical resonator

Abstract

We present a generalized theoretical analysis of the vibration of a micro/nano bridge resonator with a particle at an arbitrary location by considering the combined effect of the beam stiffness and string tension in the resonator. By combining resonant frequencies of at most three consecutive symmetric vibration modes, the developed model can unambiguously resolve the particle mass and position. The methodology is verified using published results. The finding is further validated numerically by finite element modeling using a microbridge with and without an added particle, which proves that the method resolves the particle mass and position with high accuracy.