The effect of two temperatures on a FG nanobeam induced by a sinusoidal pulse heating

Ashraf M. Zenkour , Ahmed E. Abouelregal

Abstract

The present investigation is concerned with the effect of two temperatures on functionally graded (FG) nanobeams subjected to sinusoidal pulse heating sources. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the FG nanobeam is fully ceramic whereas the lower surface is fully metal. The generalized two-temperature nonlocal theory of thermoelasticity in the context of Lord and Shulman\'s (LS) model is used to solve this problem. The governing equations are solved in the Laplace transformation domain. The inversion of the Laplace transformation is computed numerically using a method based on Fourier series expansion technique. Some comparisons have been shown to estimate the effects of the nonlocal parameter, the temperature discrepancy and the pulse width of the sinusoidal pulse. Additional results across the thickness of the nanobeam are presented graphically.

Key Words

thermoelasticity; two temperatures; FG nanobeam; nonlocal theory; sinusoidal pulse

Address

Ashraf M. Zenkour — Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia, Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh 33516, Egypt
Ahmed E. Abouelregal — Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt, Department of Mathematics, College of Science and Arts, University of Aljouf, El-Qurayat, Saudi Arabia

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