Analyse of the Free Transverse Vibrations of a Carbon Nanotube Resting on a Winkler Foundation Exposed to a Thermal Load and an Axial Magnetic Field

Abstract

In this paper, we study the free transverse vibrational behaviour of a nanotube resting on an elastic Winkler foundation when subjected to an axial magnetic field and/or a thermal field. The equation of transverse motion of the nanotube is determined on the basis of non-local Eringen elasticity and Euller-Bernoulli beam theory. By exploiting this equation and the boundary conditions, we determine a homogeneous system whose eigenvalues have been determined using the Newton-Raphson algorithm. In this study, the effects of the non-local parameter, the elastic foundation, the axial magnetic field and the thermal load at high temperature on the linear natural frequencies were examined and identified numerically and/or graphically. At the end of this work, the magnetic field is used to eliminate the decrease in the natural vibration frequencies of a nanotube undergoing a change in temperature. In the course of this work, all the results are compared with those of the existing literature and are in good agreement. Magnetic field strengths, temperature variations, elastic foundation stiffness and nonlocal parameter values are taken from existing literature.