The axial vibration of boron nitride nanorods based on nonlocal elasticity theory

In this thesis, axial bars were modeled on the nano scale and longitudinal free vibration analysis was performed. As is known, the behavior of the micro and nano-scale models of continuous systems under mechanical constraints can not be explained by the classical theory of elasticity. The internal characteristic dimensions of the micro- and nano-scale construction are included in the solution of the vibration problem. For this reason, vibration analysis of nanoblocks was carried out by adding dimension effect. The dominant equation of the vibration under the dimensional effect is obtained by using the nonlocal elasticity theory. The obtained equation is solved and applied to the bars of different supporting types modeled from the boron nitride nanotubes which are encountered extensively in the discipline of nanotechnology. The frequency values of the axial nanobranches in different modes are calculated. The influence of the nano-bar length and the supporting condition on the vibration frequency values is investigated. When the numerical results are examined, it can be said that the most important result to say is the decrease of the frequency of vibration of the increase of non-local expression. It has been observed that as the number of modes increases, the frequency of the non-locality decreases further. On the other hand, as the length of the nano-bar decreases, the non-local effect of frequency reduction is greater. It is the most important result in this study that it is necessary to consider dimension effect in the design of axial rod based nano devices.