Effect of harmonically varying heat on FG nanobeams in the context of a nonlocal two-temperature thermoelasticity theory

Abstract

The effect of two temperatures on functionally graded nanobeams due to harmonically varying heat is investigated. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel power-law distribution in terms of the volume fractions of the metal and ceramic constituents. The generalised thermoelasticity model based upon Green and Naghdi’s theory as well as the nonlocal thin beam theory is used to solve this problem. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique, the inversion of Laplace transform is made numerically. Some comparisons have been shown to present the effect of the nonlocal parameter, the temperature discrepancy parameter and the angular frequency of thermal vibration on all the studied field quantities. Additional results across the thickness of the nanobeam are presented graphically.

Keywords:

• thermoelasticity without energy dissipation
• two temperatures
• FG nanobeam
• harmonically varying heat
• a nonlocal beam theory