Axial and torsional vibration analyses of silica carbide and boron nitride nanotubes under different elastic medium effects

In this study, axial and torsional vibration analyses of nanorods embedded in an elastic medium against external forces have been presented. As it is known, to perform the mechanical analyses of the continuous models of nano scaled systems by employing classical theories does not reveal accurate results. For this, various higher-order continuum theories have been developed and used in the mechanical analyses of atomic scaled structures. The nonlocal elasticity theory that is one of the higher-order continuum theories has been taken into account in the axial and torsional vibration problems. The rod element is modelled with different materials such as silica carbide nanotube and boron nitrite nanotube that are important in nanotechnology science. The governing equations of these rod models have been obtained via the variational algebra and they have been solved by both the separation of variables and the finite element method. As a numerical result, the torsional and axial vibration frequencies of the nano scaled rods have been calculated under various parameters such as element sizes, nonlocal parameters, mode number, elastic medium stiffness and attachment. On the other hand, the results calculated by utilizing analytical method (separation of variables) and the numerical method (finite elements) have been compared and the usability of the finite element method for the problem type examined has been discussed. Moreover, finite element results are presented for several vibration analysis that are not obtained result analytically. It has been aimed to understand the dynamic behaviour of the mechanical models of nano scaled systems through the discussions that were performed by considering the numerical results.