Determination of vibration frequencies of nanoscale rod systems

In this thesis study, free vibration of nano-sized axial rods was investigated. The states of the materials studied at nanoscale under mechanical effects cannot be explained by classical elasticity theory since the internal characteristic dimensions of the nanoscale material will also be included in the calculations. For this reason, free vibration calculations of nano-sized rods will be examined with the non-local elasticity theory under the effect of size. The equations obtained by the classical theory of elasticity and the nonlocal elasticity theory were investigated with Carbon Nanotube (CNT), Gold Nanotube (AuNT), Silver Nanotube (AgNT) and Nickel Nanotube (NiNT) materials according to different support conditions. Using materials with different lengths, cross-sectional areas and support conditions, their effects on vibration frequency are examined with tables and graphics. According to the results examined, it was observed that the vibration frequency decreased as the rod length increased. It was found that as the nonlocal expression increased, the vibration frequency decreased, and the increase in the number of modes increased the frequency amplifying effect of the nonlocal expression. It has been observed that the increase in rod length increases the frequency amplifying effect of the nonlocal expression. As a result, it has been obtained that the size effect should be taken into account in the design of devices modeled in nanoscale.