Lateral vibration of an axially moving thermoelastic nanobeam subjected to an external transverse excitation

Osama Moaaz; Ahmed E. Abouelregal; Fahad Alsharari; Osama Moaaz; Ahmed E. Abouelregal; Fahad Alsharari

doi:10.3934/math.2023118

AIMS Mathematics

2023, Volume 8, Issue 1: 2272-2295. doi: 10.3934/math.2023118

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Lateral vibration of an axially moving thermoelastic nanobeam subjected to an external transverse excitation

1.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51482, Saudi Arabia
2.
Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 77455, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 12 September 2022 Revised: 08 October 2022 Accepted: 08 October 2022 Published: 31 October 2022
MSC : 65M60, 74A35, 74F05, 80A19

This paper gives a mathematical formulation for the transverse resonance of thermoelastic nanobeams that are simply supported and compressed with an initial axial force. The nonlocal elasticity concept is used to analyze the influence of length scale with the dual-phase-lag (DPL) heat transfer theory. The nanobeam is due to a changing thermal load and moves in one direction at a constant speed. The governing motion equation for the nonlocal Euler-Bernoulli (EB) beam hypothesis can also be derived with the help of Hamilton's principle and then solved by means of the Laplace transform technique. The impacts of nonlocal nanoscale and axial velocity on the different responses of the moving beam are investigated. The results reveal that phase delays, as well as the nonlocal parameter and external excitation load, have a substantial impact on the system's behavior.
- nonlocal theory,
- moving beams,
- phase-lag,
- external load,
- EB theory
Citation: Osama Moaaz, Ahmed E. Abouelregal, Fahad Alsharari. Lateral vibration of an axially moving thermoelastic nanobeam subjected to an external transverse excitation[J]. AIMS Mathematics, 2023, 8(1): 2272-2295. doi: 10.3934/math.2023118

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Abstract

This paper gives a mathematical formulation for the transverse resonance of thermoelastic nanobeams that are simply supported and compressed with an initial axial force. The nonlocal elasticity concept is used to analyze the influence of length scale with the dual-phase-lag (DPL) heat transfer theory. The nanobeam is due to a changing thermal load and moves in one direction at a constant speed. The governing motion equation for the nonlocal Euler-Bernoulli (EB) beam hypothesis can also be derived with the help of Hamilton's principle and then solved by means of the Laplace transform technique. The impacts of nonlocal nanoscale and axial velocity on the different responses of the moving beam are investigated. The results reveal that phase delays, as well as the nonlocal parameter and external excitation load, have a substantial impact on the system's behavior.

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