Nonlocal Frequency Analysis of Nanosensors with Attached Distributed Biomolecules with Different Boundary Conditions

Abstract

Nanosensors are simple engineering devices designed to detect and convey informations about nanoparticles and biomolecules. The nanosized mass sensors are based on the fact that the resonant frequency is sensitive to the resonator and the attached mass. The change of the attached mass on the resonator causes the resonant frequency to deviate from its original value. The key challenge in mass detection is in quantifying the changes in the resonant frequencies due to the added masses. The present note deals with the variational problem of the nanotube bounded at the ends, with translational and elastic constraints, and attached mass, located in a generic position. Closed-form non local frequency expression is derived; the resonant frequencies and corresponding shift frequencies are calculated and numerical results for different boundary conditions are illustrated.