Vibration of horn-shaped carbon nanotube with attached mass via nonlocal elasticity theory

This paper studies free vibration of horn-shaped single-walled carbon nanotube (SWCNT) carrying a nanoparticle, which is used to model a mass sensor. A non-uniform cantilever with a concentrated mass at the free end is analyzed according to the nonlocal Euler–Bernoulli beam theory. A governing equation of a horn-shaped SWCNT-based mass sensor is established. The transfer function method incorporating with the perturbation method is utilized to obtain the natural frequencies of a nonlocal Euler–Bernoulli beam with an attached nanoparticle. The effects of the geometry parameter, the nonlocal parameter and the attached mass on the natural frequencies or frequency shift are discussed. Obtained results show that the SWCNT-based mass sensor becomes more sensitive to the frequency shift due to the attached mass when the free end becomes sharper. In addition, there exists a horn-shaped SWCNT with special geometry, for which the fundamental frequencies are independent of size effect.