{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T01:34:14Z","timestamp":1778376854516,"version":"3.51.4"},"reference-count":54,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,2]],"date-time":"2020-08-02T00:00:00Z","timestamp":1596326400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>At present, with the development in nanotechnology, nanostructures with temperature-dependent properties have been used in nano-electromechanical systems (NEMS). Thus, introducing an accurate mathematical model of nanobeams with temperature-dependent properties is a major and important topic for the design of NEMS. This paper aims to discuss nonlocal nanobeams analysis depending on the theories of Euler\u2013Bernoulli and modified couple-stress (MCS). It also is assumed that the thermal conductivity of the nanobeam is dependent on the temperature. Physical fields of the nanobeam are obtained utilizing Laplace transform and state-space techniques. The effects of the size and nonlocal parameters, variability of thermal conductivity and couple stress on various distributions are presented graphically and studied in detail. Numerical results are presented as application scales and the design of nanoparticles, nanoscale oscillators, atomic force microscopes, and nanogenerators, in which nanoparticles as nanobeams act as essential and basic elements.<\/jats:p>","DOI":"10.3390\/sym12081276","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T07:45:57Z","timestamp":1596440757000},"page":"1276","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":101,"title":["The Response of Nanobeams with Temperature-Dependent Properties Using State-Space Method via Modified Couple Stress Theory"],"prefix":"10.3390","volume":"12","author":[{"given":"Ahmed E.","family":"Abouelregal","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 77413, Saudi Arabia"},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1063\/1.1722351","article-title":"Thermoelasticity and irreversible thermo-dynamics","volume":"27","author":"Biot","year":"1956","journal-title":"J. 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