{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:34:31Z","timestamp":1773801271395,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T00:00:00Z","timestamp":1679875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, the effects of laser light on the heat transfer of a thin beam heated by an applied current and voltage are investigated. Laser heating pulses are simulated as endogenous heat sources with discrete temporal properties. The heat conduction equation is developed using the energy conservation equation and the modified Moore\u2013Gibson\u2013Thompson (MGT) heat flow vector. Thermal and structural analysis of Euler\u2013Bernoulli microbeams is provided with the support of visco-Pasternak\u2019s base with three parameters. Using the Laplace transform method, an approximation of an analytical solution is found for the field variables being examined. A comparison was made of the impacts of laser pulse length, the three foundation coefficients, and the thermal parameters on the responses to changes in measured thermophysical fields, such as deflection and temperature.<\/jats:p>","DOI":"10.3390\/sym15040814","type":"journal-article","created":{"date-parts":[[2023,3,28]],"date-time":"2023-03-28T02:58:21Z","timestamp":1679972301000},"page":"814","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Generalized MGT Heat Transfer Model for an Electro-Thermal Microbeam Lying on a Viscous-Pasternak Foundation with a Laser Excitation Heat Source"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3363-7924","authenticated-orcid":false,"given":"Ahmed E.","family":"Abouelregal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1552-3763","authenticated-orcid":false,"given":"Marin","family":"Marin","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1167-2430","authenticated-orcid":false,"given":"Sameh S.","family":"Askar","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/17797179.2014.882141","article-title":"Effect of harmonically varying heat on FG nanobeams in the context of a nonlocal two-temperature thermoelasticity theory","volume":"23","author":"Zenkour","year":"2014","journal-title":"Euro. J. Comp. Mech."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1126\/science.290.5496.1532","article-title":"Nanoelectromechanical Systems","volume":"290","author":"Craighead","year":"2000","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1821","DOI":"10.1007\/s10483-022-2917-7","article-title":"Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading","volume":"43","author":"Li","year":"2022","journal-title":"Appl. Math. Mech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"415","DOI":"10.12989\/sem.2013.48.3.415","article-title":"Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory","volume":"48","author":"LI","year":"2013","journal-title":"Struc. Eng. Mech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/j.apm.2022.05.044","article-title":"Free vibration of self-powered nanoribbons subjected to thermal-mechanical-electrical fields based on a nonlocal strain gradient theory","volume":"110","author":"Li","year":"2022","journal-title":"Appl. Math. Model."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s42417-022-00582-0","article-title":"Free Vibration of Axially Traveling Moderately Thick FG Plates Resting on Elastic Foundations","volume":"11","author":"Sui","year":"2023","journal-title":"J. Vib. Eng. Technol."},{"key":"ref_7","first-page":"168","article-title":"Bernoulli-Euler beam unsteady bending model with consideration of heat and mass transfer","volume":"9","author":"Zemskov","year":"2023","journal-title":"J. Appl. Comp. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3648","DOI":"10.3390\/ijms12063648","article-title":"Micro electromechanical systems (MEMS) based microfluidic devices for biomedical applications","volume":"12","author":"Ashraf","year":"2011","journal-title":"Int. J. Mol. Sci."},{"key":"ref_9","first-page":"7820130","article-title":"Free and forced vibration of the moderately thick laminated composite rectangular plate on various elastic Winkler and Pasternak foundations","volume":"2017","author":"Shi","year":"2017","journal-title":"Shock Vibr."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1007\/s00419-022-02112-6","article-title":"Unsteady elastic diffusion bending model for a Timoshenko beam on a Winkler foundation","volume":"92","author":"Zemskov","year":"2022","journal-title":"Arch. Appl. Mech."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Altenbach, H., Eremeyev, V.A., and Igumnov, L.A. (2021). Multiscale Solid Mechanics. Advanced Structured Materials, Springer.","DOI":"10.1007\/978-3-030-54928-2"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"221","DOI":"10.31803\/tg-20180214212115","article-title":"The vibration of nanobeam resting on elastic foundation using modified couple stress theory","volume":"12","author":"Togun","year":"2018","journal-title":"Teh. Glas."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2894","DOI":"10.1177\/1077546317695463","article-title":"Multi-frequency excitation of microbeams supported by Winkler and Pasternak foundations","volume":"24","author":"Saadatnia","year":"2017","journal-title":"J. Vibr. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1109\/JMEMS.2016.2542338","article-title":"Highly Tunable Electrothermally and Electrostatically Actuated Resonators","volume":"25","author":"Hajjaj","year":"2016","journal-title":"J. Microelectromechanical Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s10999-019-09478-6","article-title":"Size-dependent electromechanical responses of a bilayer piezoelectric microbeam","volume":"16","author":"Liu","year":"2020","journal-title":"Int. J. Mech. Mater. Design."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8","DOI":"10.22342\/jims.28.1.1036.8-18","article-title":"Hollow cylinder with thermoelastic modelling by reduced differential transform","volume":"28","author":"Pimpare","year":"2022","journal-title":"J. Indones. Math. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1063\/1.1722351","article-title":"Thermoelsticity and Irreversible Thermodynamics","volume":"27","author":"Biot","year":"1956","journal-title":"J. Appl. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0022-5096(67)90024-5","article-title":"A generalized dynamic theory of thermoelasticity","volume":"15","author":"Lord","year":"1967","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00045689","article-title":"Thermoelasticity","volume":"2","author":"Green","year":"1972","journal-title":"J. Elast."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1098\/rspa.1991.0012","article-title":"A re-examination of the basic postulates of thermomechanics","volume":"432","author":"Green","year":"1991","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1080\/01495739208946136","article-title":"On undamped heat waves in an elastic solid","volume":"15","author":"Green","year":"1992","journal-title":"J. Therm. Stress."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF00044969","article-title":"Thermoelasticity without energy dissipation","volume":"31","author":"Green","year":"1993","journal-title":"J. Elast."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4020","DOI":"10.1177\/1081286519862007","article-title":"Moore\u2013Gibson\u2013Thompson thermoelasticity","volume":"24","author":"Quintanilla","year":"2019","journal-title":"Math. Mech. Solids."},{"key":"ref_24","first-page":"100006","article-title":"Moore-Gibson-Thompson thermoelasticity with two temperatures","volume":"1","author":"Quintanilla","year":"2020","journal-title":"Appl. Eng. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/s00161-022-01170-z","article-title":"Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model","volume":"35","author":"Abouelregal","year":"2023","journal-title":"Continuum Mech. Thermodyn."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Abouelregal, A.E., Rayan, A., and Mostafa, D.M. (2022). Transient responses to an infinite solid with a spherical cavity according to the MGT thermo-diffusion model with fractional derivatives without nonsingular kernels. Waves Random Complex Media.","DOI":"10.1080\/17455030.2022.2147242"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Moaaz, O., Abouelregal, A.E., and Alsharari, F. (2022). Analysis of a transversely isotropic annular circular cylinder immersed in a magnetic field using the Moore\u2013Gibson\u2013Thompson thermoelastic model and generalized Ohm\u2019s law. Mathematics, 10.","DOI":"10.3390\/math10203816"},{"key":"ref_28","first-page":"1","article-title":"Thermoelasticity of Moore\u2013Gibson\u2013Thompson type with history dependence in the temperature","volume":"120","author":"Conti","year":"2020","journal-title":"Asymptot. Anal."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Gupta, S., Dutta, R., Das, S., and Pandit, D.K. (2022). Hall current effect in double poro-thermoelastic material with fractional-order Moore\u2013Gibson\u2013Thompson heat equation subjected to Eringen\u2019s nonlocal theory. Waves Random Complex Media.","DOI":"10.1080\/17455030.2021.2021315"},{"key":"ref_30","first-page":"375","article-title":"On existence and uniqueness in thermoelasticity of micropolar bodies, Comptes rendus de l\u2019Acad\u00e9mie des Sciences Paris","volume":"321","author":"Marin","year":"1995","journal-title":"S\u00e9rie II B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0020-7225(97)00019-0","article-title":"Thermoelasticity of initially stressed bodies. Asymptotic equipartition of energies","volume":"36","author":"Marin","year":"1998","journal-title":"Int. J. Eng. Sci."},{"key":"ref_32","unstructured":"Het\u00e9nyi, M. (1971). Beams on Elastic Foundation: Theory with Applications in the Fields of Civil and Mechanical Engineering, University of Michigan."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1007\/s11071-019-04977-9","article-title":"Elastic and viscoelastic foundations: A review on linear and nonlinear vibration modeling and applications","volume":"97","author":"Younesian","year":"2019","journal-title":"Nonlinear Dyn."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.apm.2020.03.031","article-title":"Analytical solution considering the tangential effect for an infinite beam on a viscoelastic Pasternak foundation","volume":"85","author":"Miao","year":"2020","journal-title":"Appl. Math. Model."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.ijengsci.2017.08.016","article-title":"On the analysis of microbeams","volume":"121","author":"Demir","year":"2017","journal-title":"Int. J. Eng. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2408","DOI":"10.1080\/15376494.2020.1739357","article-title":"Size-dependent buckling analysis of nanobeams resting on two-parameter elastic foundation through stress-driven nonlocal elasticity model","volume":"28","author":"Darban","year":"2021","journal-title":"Mech. Adv. Mater. Struct."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3013","DOI":"10.1007\/s12206-009-0816-3","article-title":"Response of the beams on random Pasternak foundations subjected to harmonic moving loads","volume":"23","author":"Younesian","year":"2009","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"111301","DOI":"10.1115\/1.3153580","article-title":"On the analysis of short-pulse laser heating of metals using the dual phase lag heat conduction model. ASME J","volume":"131","author":"Ramadan","year":"2009","journal-title":"Heat Transf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.applthermaleng.2014.01.024","article-title":"Estimation of energy absorption rate and temperature distributions in short-pulse laser heating of metals with a dual-phase-lag model","volume":"65","author":"Lee","year":"2014","journal-title":"Appl. Therm. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.amc.2018.01.026","article-title":"Numerical inversion of the Laplace transform and its application to fractional diffusion","volume":"327","author":"Campos","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(79)90025-1","article-title":"Numerical inversion of the Laplace transform: A survey and comparison of methods","volume":"33","author":"Davies","year":"1979","journal-title":"J. Comput. Phys."},{"key":"ref_42","first-page":"9805","article-title":"Laplace transform inversion on the real line is truly ill-conditioned, Appl","volume":"219","author":"Gzyl","year":"2013","journal-title":"Math. Comput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/0377-0427(84)90075-X","article-title":"A method for the numerical inversion of Laplace transforms","volume":"10","author":"Honig","year":"1984","journal-title":"J. Comput. Appl. Math."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1145\/361953.361969","article-title":"Algorithm 368: Numerical inversion of Laplace transforms [D5]","volume":"13","author":"Stehfest","year":"1970","journal-title":"Commun. ACM"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1145\/355598.362787","article-title":"Remark on algorithm 368: Numerical inversion of Laplace transforms","volume":"13","author":"Stehfest","year":"1970","journal-title":"Commun. ACM"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1515\/jacsm-2015-0006","article-title":"Application of Numerical Laplace Inversion Methods in Chemical Engineering with Maple\u00ae","volume":"7","author":"Szukiewicz","year":"2015","journal-title":"J. Appl. Comput. Sci. Methods"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1007\/s00161-017-0585-7","article-title":"The effect of a dipolar structure on the H\u00f6lder stability in Green\u2013Naghdi thermoelasticity, Contin","volume":"29","author":"Marin","year":"2017","journal-title":"Mech. Thermodyn."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1186\/s13661-020-01401-9","article-title":"New analytical method based on dynamic response of planar mechanical elastic systems","volume":"2020","author":"Sorin","year":"2020","journal-title":"Bound. Val. Probl."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Abouelregal, A.E., and Marin, M. (2020). The response of nanobeams with temperature-dependent properties using state-space method via modified couple stress theory. Symmetry, 12.","DOI":"10.3390\/sym12081276"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1080\/16583655.2020.1751963","article-title":"On the decay of exponential type for the solutions in a dipolar elastic body","volume":"14","author":"Marin","year":"2020","journal-title":"J. Taibah Univ. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/4\/814\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:04:17Z","timestamp":1760123057000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/4\/814"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,27]]},"references-count":50,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["sym15040814"],"URL":"https:\/\/doi.org\/10.3390\/sym15040814","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,27]]}}}