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Vibration of FG nanobeams induced by sinusoidal pulse-heating via a nonlocal thermoelastic model

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Abstract

The vibration of functionally graded (FG) nanobeams subjected to a sinusoidal pulse-heating source is investigated. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the FG nanobeam is pure ceramic, whereas the lower surface is pure metal. The generalized nonlocal thermoelasticity model based on Lord and Shulman’s theory is used to solve this problem. An analytical technique based on Laplace transform is used to calculate the vibration of deflection and temperature. The inverse Laplace transforms are computed numerically using Fourier expansion techniques. A comparison between the obtained results from the nonlocal theory and those from the local theory of coupled thermoelasticity is presented. The effect of the nonlocal parameter, the pulse width of the sinusoidal pulse, is studied on the lateral vibration, the temperature and the displacement of the nanobeam. Additional results across the thickness of the nanobeam are presented graphically.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Ashraf M. Zenkour

  2. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafr El-Sheikh, 33516, Egypt

    Ashraf M. Zenkour

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Ahmed E. Abouelregal

Authors
  1. Ashraf M. Zenkour
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  2. Ahmed E. Abouelregal
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Correspondence to Ashraf M. Zenkour.

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Zenkour, A.M., Abouelregal, A.E. Vibration of FG nanobeams induced by sinusoidal pulse-heating via a nonlocal thermoelastic model. Acta Mech 225, 3409–3421 (2014). https://doi.org/10.1007/s00707-014-1146-9

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  • DOI: https://doi.org/10.1007/s00707-014-1146-9

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