The Vibration of Nano-Beam Subjected to Thermal Shock and Moving Heat Source with Constant Speed

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.