{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:10:07Z","timestamp":1792789807458,"version":"4.5.0"},"reference-count":47,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T00:00:00Z","timestamp":1789603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12472165"],"award-info":[{"award-number":["12472165"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Natural Science Foundation of China","award":["12572161"],"award-info":[{"award-number":["12572161"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Natural Science Foundation of China","award":["12102222"],"award-info":[{"award-number":["12102222"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"award":["12472165"],"award-info":[{"award-number":["12472165"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["12572161"],"award-info":[{"award-number":["12572161"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["12102222"],"award-info":[{"award-number":["12102222"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Shanghai Gaofeng Project for University Academic Program Development, and State Key Laboratory of Flexible Electronics Technology, Tsinghua University","id":[{"id":"https:\/\/ror.org\/03cve4549","id-type":"ROR","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/03cve4549","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>The quality factor is a key metric for evaluating the performance of micro-electro-mechanical and nano-electro-mechanical system resonators. Although reducing device dimensions enhances resonator sensitivity, it also intensifies energy dissipation, thereby degrading the quality factor. Among the dominant dissipation mechanisms in micro-\/nano-resonators, support loss is strongly influenced by surface effects at small scales, particularly the surface elastic modulus and initial surface stress. In this study, support loss in a double-clamped micro-\/nano-beam resonator with surface effects incorporated is investigated. A dynamic model incorporating the surface elastic modulus and initial surface stress is developed based on Euler\u2013Bernoulli beam theory and Gurtin\u2013Murdoch surface elasticity theory. A quality-factor calculation method is then established by combining elastic wave radiation in the supports with an energy-based formulation. The theoretical predictions are validated using a three-dimensional finite element model comprising the resonator with a surface layer, supports, and a perfectly matched layer. Further, the effects of the surface elastic modulus, initial surface stress, characteristic size, and dimensionless geometric parameters on support loss are examined. The results show that the surface elastic modulus and initial surface stress increase support loss and reduce the quality factor, with the initial surface stress exhibiting the stronger influence. The influence of these parameters becomes more pronounced as the characteristic size decreases, and variations in the length-to-thickness and width-to-thickness ratios further modify their contribution to support loss. Mechanistically, surface effects alter the effective bending stiffness and axial force, thereby changing the dynamic loads transmitted to the supports and resulting elastic-wave radiation. These findings provide theoretical insights for the design of high-quality-factor micro-\/nano-devices.<\/jats:p>","DOI":"10.3390\/nano16181175","type":"journal-article","created":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T11:41:35Z","timestamp":1789645295000},"page":"1175","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Impact of Surface Effects on Support-Loss Mechanisms in Micro-\/Nano-Beam Resonators"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2921-9212","authenticated-orcid":false,"given":"Yonglin","family":"Chen","sequence":"first","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Xiaobin","family":"Jian","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Shuolong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Guangyue","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1796-2209","authenticated-orcid":false,"given":"Weijian","family":"Jiao","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Siyu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China"},{"name":"State Key Laboratory of Flexible Electronics Technology, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"061101","DOI":"10.1063\/1.1927327","article-title":"Nanoelectromechanical Systems","volume":"76","author":"Ekinci","year":"2005","journal-title":"Rev. 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