Vibration of double-walled carbon nanotube based nanomechanical sensor with initial axial stress

This paper studies free vibration of double-walled carbon nanotubes (DWCNTs) based nanomechanical sensor under initial axial stress. A bridged DWCNT carrying a nanoparticle at any position of the outer tube is modeled as two clamped nonlocal Euler–Bernoulli beams, and the interaction between two tubes is governed by van der Waals force. For comparison, a bridged single-walled carbon nanotube (SWCNT) based nanomechanical sensor is considered in a similar way. Using the transfer function method, the critical buckling stress and natural frequencies of these nanomechanical sensors are computed. Under small initial stress, the effects of the attached nanoparticle, and the small scale parameter on the frequency shift are discussed. The obtained results show that when the mass of the nanoparticle increases or its location is closed to the beam center, the natural frequency decreases, but frequency shift increases. Initial tensile stress increases the natural frequency, while initial compressive stress decreases the natural frequency. In comparison with SWCNT sensor, DWCNT is more stable, but less sensitive for smaller attached mass. Obtained results are helpful to the design of DWCNT-based resonator as nanomechanical sensor.