Nonlocal frequency analysis of nanosensors with different boundary conditions and attached distributed biomolecules: an approximate method

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 paper deals with the free vibration analysis of a single-walled carbon nanotube with attached distributed mass, located in a generic position. According to the nonlocal Euler–Bernoulli beam theory, a system of three equations of motion, of a single-walled carbon nanotube with an added mass, is derived. Using an approximate method, generalized nondimensional calibration constants are derived for an explicit relationship between the added mass, the nonlocal parameter, and the frequency shift. Numerical results for different boundary conditions and nonlocal coefficient are performed in order to evaluate the effect of the added mass.