Free vibration analysis of carbon nanotube reinforced plates

In this thesis study, axial rods and skew plates are modeled at nano scale and longitudinal free vibration analysis was performed. The behavior of the micro and nano-scale models of continuous systems under mechanical influences cannot be explained by classical elasticity theory since the internal characteristic dimensions of micro and nano scale structure will be included in the solution of vibration problem. For this reason, vibration analysis of nanorods is performed by including the size effect. The equation of vibration in the effect of dimension is obtained by the theory of non-local elasticity. The obtained equation is solved and applied to the rods in different boundary conditions for Carbon Nanotube (CNT), Boron Nitride Nanotube (BNNT) and Silica Carbide Nanotube (SiCNT) materials. Also, equation of motion of CNT reinforced skew plates is obtained. Frequency values of axial rods and skew plates in different parameters are calculated. When the results were examined, it is obtained that the increase in non-local expression decreases the vibration frequency. As the number of modes increased, the non-local expression decreased the frequency significantly. As the rod length increases, the frequency-enhancing effect of the non-local expression increases. When designing nano devices modeled as axial rods, it is concluded that size effect should be taken into consideration. key words:Axial nanorod, Carbon nanotube, Boron nitride nanotube, Silica carbide nanotube, Non-local elasticity theory, Size effect, Nanotechnology, Free vibration.