Analytical Analysis for Free Vibration of Different Arrangements of BNNTs under Initially Stress

In this research, an analytical analysis is used to investigate the effects of elasticity modulus of different arrangements (zigzag, chiral, armchair) on the vibrations responses of boron nitride nanotubes (BNNTs) under initially stress. By using the Euler– Bernoulli and Timoshenko nonlocal elasticity theories, the governing equation of motion and boundary conditions are derived via Hamilton’s principle. The analysis considers beams with four different boundary conditions, namely pinned-pinned, fixed-fixed, pinned-fixed and fixed-free. The elasticity modulus of zigzag, armchair and chiral is studied and the effects of these arrangements on natural frequency are investigated. Finally, the effect of various parameters such as nanotube diameter, initial stress, nonlocal parameter and geometric parameters of BNNTs on the natural frequency of zigzag, armchair and chiral BNNTs has been studied. The results show that the natural frequency is decreased when nonlocal parameter and initial stress increase. Furthermore, we observe an increase in natural frequency as nanotube diameter is increased up to 0.6nm while afterwards there is no noticeable change in natural frequency.