Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation
This study aims to investigate the behavior of viscoelastic materials exhibiting complex mechanical behavior characterized by both elastic and viscous properties. They are widely used in various engineering applications, such as structural components, transportation systems, energy storage devices,...
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| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/2/118 |
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| author | Yahya Ahmed Adam Zakria Osman Abdalla Adam Osman Muntasir Suhail Mohammed Nour A. Rabih |
| author_facet | Yahya Ahmed Adam Zakria Osman Abdalla Adam Osman Muntasir Suhail Mohammed Nour A. Rabih |
| author_sort | Yahya Ahmed |
| collection | DOAJ |
| description | This study aims to investigate the behavior of viscoelastic materials exhibiting complex mechanical behavior characterized by both elastic and viscous properties. They are widely used in various engineering applications, such as structural components, transportation systems, energy storage devices, microelectromechanical systems (MEMS), and earthquake research and detection. Accurate modeling of viscoelastic behavior is crucial for predicting its performance under dynamic loading conditions. In this study, we modify the equations governing the thermoelastic resistance to describe the thermal variables of a thermoelastic micro-beam supported by a two-parameter Pasternak viscoelastic foundation by using a fractional Moore–Gibson–Thompson (MGT) model in the context of non-locality. The temperature, bending displacement, and moment were computed and graphically displayed using the Laplace transform method. Different theoretical approaches have been compared in order to explain how the phase delay affects physical phenomena. Numerical results show that the wave fluctuations of variables in thermoelastic micro-beams are slightly smaller for the studied model and that the speed of these plane waves depends on fractional and non-local parameters. |
| format | Article |
| id | doaj-art-2fbbe50fcac3432ba459787f31db7d89 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-2fbbe50fcac3432ba459787f31db7d892025-08-20T02:44:42ZengMDPI AGFractal and Fractional2504-31102025-02-019211810.3390/fractalfract9020118Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak FoundationYahya Ahmed0Adam Zakria1Osman Abdalla Adam Osman2Muntasir Suhail3Mohammed Nour A. Rabih4Department of Mathematics, College of Science, Jouf University, Sakaka 2014, Saudi ArabiaDepartment of Mathematics, College of Science, Jouf University, Sakaka 2014, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaThis study aims to investigate the behavior of viscoelastic materials exhibiting complex mechanical behavior characterized by both elastic and viscous properties. They are widely used in various engineering applications, such as structural components, transportation systems, energy storage devices, microelectromechanical systems (MEMS), and earthquake research and detection. Accurate modeling of viscoelastic behavior is crucial for predicting its performance under dynamic loading conditions. In this study, we modify the equations governing the thermoelastic resistance to describe the thermal variables of a thermoelastic micro-beam supported by a two-parameter Pasternak viscoelastic foundation by using a fractional Moore–Gibson–Thompson (MGT) model in the context of non-locality. The temperature, bending displacement, and moment were computed and graphically displayed using the Laplace transform method. Different theoretical approaches have been compared in order to explain how the phase delay affects physical phenomena. Numerical results show that the wave fluctuations of variables in thermoelastic micro-beams are slightly smaller for the studied model and that the speed of these plane waves depends on fractional and non-local parameters.https://www.mdpi.com/2504-3110/9/2/118thermoelasticnon-localmicro-beamsnumerical resultsfoundationPasternak |
| spellingShingle | Yahya Ahmed Adam Zakria Osman Abdalla Adam Osman Muntasir Suhail Mohammed Nour A. Rabih Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation Fractal and Fractional thermoelastic non-local micro-beams numerical results foundation Pasternak |
| title | Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation |
| title_full | Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation |
| title_fullStr | Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation |
| title_full_unstemmed | Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation |
| title_short | Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation |
| title_sort | fractional moore gibson thompson heat conduction for vibration analysis of non local thermoelastic micro beams on a viscoelastic pasternak foundation |
| topic | thermoelastic non-local micro-beams numerical results foundation Pasternak |
| url | https://www.mdpi.com/2504-3110/9/2/118 |
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