Analytical Solution of Vibration Analysis on Fixed-Free Single-Walled Carbon Nanotube-Based Mass Sensor

Abstract

Fixed-free single-walled carbon nanotubes (SWCNTs) have attracted a lot of interest in recent years due to their suit-ability for a wide range of applications, such as field emission and vacuum microelectronic devices, nanosensors, and nanoactuators. Based on a cantilever beam-bending model with a rigid mass at the free end and mode analysis, an ana-lytical solution is developed in the present study to deal with the resonant frequency and mode shapes of a SWCNT-based mass sensor. The resonant frequency shift and mode shape of the fixed-free SWCNTs caused by the addition of a nanoscale particle to the beam tip are examined in order to explore the suitability of SWCNTs as a mass detector device. The simulation results reveal that the volume of the added particle has little effect on the first resonant frequency. In contrast, the second resonant frequency decreases with increasing the volume of the added particle. Furthermore, the resonant frequency shift of the first mode is very obvious for the amount of added mass, and the second resonant fre-quency decreases rapidly with increasing volume of added particle. Therefore, the first and second resonant frequencies can be used in the measurement of the mass of added particle and its volume, respectively.