Vibration analysis of boron nitride nanotubes by considering electric field and surface effect

In this paper, the vibrations of boron nitride nanotubes (BNNTs) are investigated by considering the electric field. To consider the size effect at nanoscale dimensions, the surface elasticity theory is exploited. The equations of motion of the BNNTs are obtained by applying Hamilton's principle, and the clamped-guided boundary conditions are also considered. The governing equations and boundary conditions are discretized using the differential quadrature method (DQM), and the natural frequency is obtained by using the eigenvalue problem solution. The results are compared with the molecular dynamic simulation in order to validate the accurate values of the surface effects. In the molecular dynamics (MD) simulation, the potential between boron and nitride atoms is considered as the Tersoff type. The Timoshenko beam model is adopted to model BNNT. The vibrations of two types of zigzag and armchair BNNTs are considered. In the result section, the effects of chirality, surface elasticity modulus, surface residual tension, surface density, electric field, length, and thickness of BNNT on natural frequency are investigated. According to the results, it should be noted that, as an efficient non-classical continuum mechanic approach, the surface elasticity theory can be used in scrutinizing the dynamic behavior of BNNTs.