Thermomechanical vibration analysis of a restrained nanobeam

Abstract

In this study, thermomechanical vibration analysis of a nanobeam model of boron nitride nanotube is performed. Displacement is allowed by placing elastic springs in the boundary conditions. The end displacements are represented by two different coefficients and the variable in the region is represented by an analytical Fourier sine function. The Stokes' transformation is used to force the boundary conditions to resemble the desired support shape. It is aimed in this study, a general eigenvalue problem that gives the thermal vibrational frequencies of a single-walled boron nitride nanotube under deformable boundary conditions is established. Unlike the studies with rigid boundary conditions found in the literature, in this study, there is no need to re-derive the system equations for each boundary condition change. The results are compared with similar results in the literature and excellent agreement is obtained. In addition, the effects of thermal load, elastic springs, small-scale parameters and elastic foundation are investigated and it is found that these effects have a negligible influences on the vibration frequencies of boron nitride nanotubes.