An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories

Abstract

The vibration of the gold microbeam resonator considering the effects of the material length scale under the temperature effect is investigated in this article. The modified couple stress theory is utilized to show the material length scale effects. The effects of temperature considering the thermoelastic damping are taken into account based on Green-Naghdi thermoelasticity theory. The Green-Naghdi coupled thermoelasticity and modified couple stress governing equations for Euler-Bernoulli beam are derived based on Hamilton’s principle. The Laplace method is utilized to solve the obtained equations. The inverse Laplace method as Talbot method is used to obtain the lateral deflection and temperature response of the microbeam in the time domain. The effects of the various parameters such as the nondimensional material length scale parameter, the thickness of the microbeam, and the initial temperature conditions, on the lateral deflection as well as temperature responses of the microbeam are studied to investigate the results. Raising the material length scale parameter and width to length ratio makes the lateral deflection of the beam decrease in the time domain. Increase in temperature shock and Poisson’s ratio makes the lateral deflection increase, and both have a direct effect on the lateral deflection in the time domain, except that this increase is linear for temperature shock. The temperature of the microbeam decreases by an increase in Poisson’s ratio and progressing in the axial direction. For the final observation, it should be noted that the couple stress has an inverse effect on the lateral deflection.