Journal of Nano Research Vol. 61

Abstract: In nano-dimension, the strength of the material is considerable, and the failure is unavoidable in a torsional mode. Because of this reason, the free and forced torsional vibrations of single-walled carbon nanotube (SWCNT) are investigated in this paper. For dynamic analysis, the moving harmonic torsional load is exerted to SWCNT. The related boundary condition and equation of motion are derived by Hamilton’s principle, and the equation is discretized by the Galerkin method. In order to demonstrate the nonlocality and small–scale effect, Eringen’s theory based on nonlocal elasticity theory is applied. A clamped-clamped (C-C) boundary condition is fitted for the end supports. The influences of the aspect ratio and mode number on the free natural frequency are investigated. Furthermore, the dynamic effects of nonlocal parameter, velocity, thickness, length, and excitation-to-natural frequencies on dimensional and nondimensional angular displacements are indicated. Moreover, the natural frequency was investigated due to the variation of the aspect ratio.

Abstract: This paper deals with a mathematical model of thermoelastic rectangular nano-beam, which is thermally loaded by thermal shock and subjected to moving heat source with constant speed. The nano-beam has been clamped-clamped and its length along the x-axis. The governing equations have been written by using the Euler–Bernoulli equation of nano-beams and the non-Fourier heat conduction with one-relaxation time. Laplace transform has been applied with respect to the time variable, and the solutions have been derived in its domain. The numerical solutions for the Silicon material have been done by using Tzou method. The results have been shown in figures for the temperature increment and the lateral deflection with various values of heat source speed to stand on its effects. Moreover, the effects of the ratio between the length and the width of the beam have been discussed. The speed of the heat source and the dimensions of the beam have significant effects on the temperature increment and the lateral deflection of the beam.