Vibration Of Carbon Nanotube-based Mass Sensor Via Nonlocal Elasticity Theory

Carbon nanotubes(CNTs) possess many remarkable physical properties, such as small scale, low weight, high rigidity, especially extraordinary sensitivity to the external situation and so on. Such features of CNTs make them possess broad prospects in the application of micro- nano scale mass sensor. This paper explores the vibrational behavior of single-walled carbon nanotubes as mass sensors via nonlocal elastic beam theory. The main achievements as follows:The transverse vibration model of uniform single-walled carbon nanotube(SWCNT) based mass sensor is established via nonlocal Timoshenko beam theory under different end supports. The vibrational behavior of uniform SWCNT is analyzed as a mass sensor. The transfer function method is used to obtain natural frequencies of the vibrating SWCNT-mass system. The effects of the nonlocal parameter, the mass and position of an attached nanoparticle, the length-to-diameter ratio of the SWCNT on natural frequencies and frequency shifts are discussed for typical end supports. O ur results show that increasing the attached mass or decreasing the length-to-diameter ratio, the frequency shift increases. The fundamental frequencies and frequency shifts rise slightly for cantilever mass sensors, but decrease for other end supports as the nonlocal parameter rises.The transverse vibration model of non-uniform cantilever SWCNT based mass sensor with a concentrated mass at the free end is established via nonlocal Euler beam theory. The vibrational behavior of non- uniform SWCNT is analyzed as a mass sensor. The transfer function method incorporating with the perturbation method is utilized to obtain the natural frequencies of the vibrating SWCNT- mass system. The influences of the geometry parameter, the nonlocal parameter and the attached mass on the natural frequencies or frequency shift are discussed. Obtained results indicate that the sensitivity of the frequency shifts due to the attached mass increases when the taper ratio becomes larger. Increasing the attached mass or decreasing the length-to-diameter ratio increases the frequency shift. In addition, there exists a non-uniform SWCNT with special taper ratio, for which the fundamental frequencies are independent of size effect.The transverse vibration model of non-uniform cantilever SWCNT based mass sensor with a concentrated mass at the free end is established via nonlocal Timoshenko beam theory. The vibrational behavior of non-uniform SWCNT is analyzed as a mass sensor. The transfer function method incorporating with the perturbation method is utilized to obtain the natural frequencies of the vibrating SWCNT-mass system. The influences of the geometry parameter, the nonlocal parameter a nd the attached mass on the natural frequencies or frequency shift are discussed. Obtained results indicate that the sensitivity to the frequency shift increases when the taper ratio becomes larger and the attached mass increases as well as the length-to-diameter ratio decreases. Increasing the taper ratio increases fundamental frequency and decreases higher order natural frequencies.This paper studies the vibrational behaviors of SWCNT based mass sensors by using nonlocal elasticity theory. The influences of the nonlocal parameter, the geometry parameter of the SWCNT and the attached mass on the vibrational behaviors are discussed. Obtained results provide a theoretical reference for the design of efficient CNT based mass sensor.