Vibration analysis of nanomechanical mass sensor using carbon nanotubes under axial tensile loads

Vibration analysis of carbon nanotube-based resonator using nonlocal elasticity theory

“…Y(x) is the deflection shape of CNT with the first mode of vibration.According to our previous study [16], the deflection shape in Eq. (12) yielded…”

“…In our previous work [16], the resonant frequencies and frequency shifts of the CNTs with attached mass were investigated by the Euler-Bernoulli beam theory. The local elastic theory does not consider about the long-range forces between atoms.…”

Carbon Nanotube-Based Nanomechanical Sensor: Theoretical Analysis of Mechanical and Vibrational Properties

“…In order to increase sensitivity of the resonators, the author Natsuki and co-workers proposed using a double end fixed CNT with applied tensile loads and investigated the possibility of application [42,43]. Figure 7 shows a schematic diagram of the clamped CNT beam, subjected to an axial force and carrying an attached concentrated mass m c .…”

“…Based on Rayleigh's energy method [42], the differential equation of CNT bending moment can be given by…”

“…Figure 7 shows a schematic diagram of the clamped CNT beam, subjected to an axial force and carrying an attached concentrated mass m c . Based on the continuum model with the Euler-Bernoulli beam, the motion equations of a freely vibrating CNT under the axial tensile load N can be given as [42] …”