Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions
Thermoelastic dynamic analysis of micro-/nano-beams is essential in the field of micro-/nano-electro-mechanical systems (MEMSs/NEMSs). However, the classical coupled thermoelastic theory is not suitable for the microscopic/nanoscopic case. As elementary parts of MEMSs/NEMSs, the size effect of micro...
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| Veröffentlicht in: | Journal of sound and vibration 2020-09, Vol.481, p.115407, Article 115407 |
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| creator | Zhao, X. Zhu, W.D. Li, Y.H. |
| description | Thermoelastic dynamic analysis of micro-/nano-beams is essential in the field of micro-/nano-electro-mechanical systems (MEMSs/NEMSs). However, the classical coupled thermoelastic theory is not suitable for the microscopic/nanoscopic case. As elementary parts of MEMSs/NEMSs, the size effect of micro-/nano-beams must be considered in their thermoelastic vibrations. This work originally explores analytical solutions of coupled thermoelastic forced vibrations of micro-/nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory. The heat conductivity equation is obtained by using the type Ⅲ Green-Naghdi theory. Coupled thermoelastic dynamic equations are decoupled by use of Green's function method and expressions of displacements, temperature fields, and thermal moments of micro-/nano-beams are derived. Furthermore, movement behaviors of an “ice core” of the temperature field are used to explain dynamic phenomena of the coupled system. Results from finite element analysis are compared with analytical solutions for verification purposes. This work primarily discusses influences of a small-scale parameter on coupled displacement and temperature fields and those of other important physical parameters, such as heating positions and height-to-length ratios of micro-/nano-beams, on system responses. |
| doi_str_mv | 10.1016/j.jsv.2020.115407 |
| format | Article |
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However, the classical coupled thermoelastic theory is not suitable for the microscopic/nanoscopic case. As elementary parts of MEMSs/NEMSs, the size effect of micro-/nano-beams must be considered in their thermoelastic vibrations. This work originally explores analytical solutions of coupled thermoelastic forced vibrations of micro-/nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory. The heat conductivity equation is obtained by using the type Ⅲ Green-Naghdi theory. Coupled thermoelastic dynamic equations are decoupled by use of Green's function method and expressions of displacements, temperature fields, and thermal moments of micro-/nano-beams are derived. Furthermore, movement behaviors of an “ice core” of the temperature field are used to explain dynamic phenomena of the coupled system. Results from finite element analysis are compared with analytical solutions for verification purposes. This work primarily discusses influences of a small-scale parameter on coupled displacement and temperature fields and those of other important physical parameters, such as heating positions and height-to-length ratios of micro-/nano-beams, on system responses.</description><identifier>ISSN: 0022-460X</identifier><identifier>EISSN: 1095-8568</identifier><identifier>DOI: 10.1016/j.jsv.2020.115407</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Beams (structural) ; Elasticity ; Exact solutions ; Finite element method ; Forced vibration ; Green's function ; Green's functions ; Green-Naghdi theory ; Heat conductivity ; Mathematical analysis ; Mechanical properties ; Mechanical systems ; Nonlocal elasticity ; Nonlocal elasticity theory ; Parameters ; Physical properties ; Size effects ; Temperature distribution ; Thermal conductivity ; Thermoelastic forced vibration ; Vibration</subject><ispartof>Journal of sound and vibration, 2020-09, Vol.481, p.115407, Article 115407</ispartof><rights>2020 Elsevier Ltd</rights><rights>Copyright Elsevier Science Ltd. Sep 1, 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-a6e845c20595e0b046f784c81e952cf068cfb931b242a19b760b086acd3b04733</citedby><cites>FETCH-LOGICAL-c325t-a6e845c20595e0b046f784c81e952cf068cfb931b242a19b760b086acd3b04733</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jsv.2020.115407$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids></links><search><creatorcontrib>Zhao, X.</creatorcontrib><creatorcontrib>Zhu, W.D.</creatorcontrib><creatorcontrib>Li, Y.H.</creatorcontrib><title>Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions</title><title>Journal of sound and vibration</title><description>Thermoelastic dynamic analysis of micro-/nano-beams is essential in the field of micro-/nano-electro-mechanical systems (MEMSs/NEMSs). However, the classical coupled thermoelastic theory is not suitable for the microscopic/nanoscopic case. As elementary parts of MEMSs/NEMSs, the size effect of micro-/nano-beams must be considered in their thermoelastic vibrations. This work originally explores analytical solutions of coupled thermoelastic forced vibrations of micro-/nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory. The heat conductivity equation is obtained by using the type Ⅲ Green-Naghdi theory. Coupled thermoelastic dynamic equations are decoupled by use of Green's function method and expressions of displacements, temperature fields, and thermal moments of micro-/nano-beams are derived. Furthermore, movement behaviors of an “ice core” of the temperature field are used to explain dynamic phenomena of the coupled system. Results from finite element analysis are compared with analytical solutions for verification purposes. This work primarily discusses influences of a small-scale parameter on coupled displacement and temperature fields and those of other important physical parameters, such as heating positions and height-to-length ratios of micro-/nano-beams, on system responses.</description><subject>Beams (structural)</subject><subject>Elasticity</subject><subject>Exact solutions</subject><subject>Finite element method</subject><subject>Forced vibration</subject><subject>Green's function</subject><subject>Green's functions</subject><subject>Green-Naghdi theory</subject><subject>Heat conductivity</subject><subject>Mathematical analysis</subject><subject>Mechanical properties</subject><subject>Mechanical systems</subject><subject>Nonlocal elasticity</subject><subject>Nonlocal elasticity theory</subject><subject>Parameters</subject><subject>Physical properties</subject><subject>Size effects</subject><subject>Temperature distribution</subject><subject>Thermal conductivity</subject><subject>Thermoelastic forced vibration</subject><subject>Vibration</subject><issn>0022-460X</issn><issn>1095-8568</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKxDAQhoMouK4-gLeCB09dJ2matnhaFl2FBS8K3kKanWJKm6xJu7D48matePQUZub7wsxPyDWFBQUq7tpFG_YLBizWNOdQnJAZhSpPy1yUp2QGwFjKBbyfk4sQWgCoeMZn5GtpVXcYjFZdElw3DsbZkLgmsc527tjVbtx1uE2GD_S9w06FSCeN8zo296b26s_pjfYuvbPKurRG1YekPiQ9qmm69oj2NiTNaPWPcknOGtUFvPp95-Tt8eF19ZRuXtbPq-Um1RnLh1QJLHmuGeRVjlADF01Rcl1SrHKmGxClbuoqozXjTNGqLkSESqH0NotwkWVzcjP9u_Puc8QwyNaNPt4dJOOcZUwUHCJFJyreEILHRu686ZU_SArymLFsZcxYHjOWU8bRuZ8cjOvvDXoZtEEbkzEe9SC3zvxjfwNXBoW4</recordid><startdate>20200901</startdate><enddate>20200901</enddate><creator>Zhao, X.</creator><creator>Zhu, W.D.</creator><creator>Li, Y.H.</creator><general>Elsevier Ltd</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20200901</creationdate><title>Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions</title><author>Zhao, X. ; Zhu, W.D. ; Li, Y.H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-a6e845c20595e0b046f784c81e952cf068cfb931b242a19b760b086acd3b04733</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Beams (structural)</topic><topic>Elasticity</topic><topic>Exact solutions</topic><topic>Finite element method</topic><topic>Forced vibration</topic><topic>Green's function</topic><topic>Green's functions</topic><topic>Green-Naghdi theory</topic><topic>Heat conductivity</topic><topic>Mathematical analysis</topic><topic>Mechanical properties</topic><topic>Mechanical systems</topic><topic>Nonlocal elasticity</topic><topic>Nonlocal elasticity theory</topic><topic>Parameters</topic><topic>Physical properties</topic><topic>Size effects</topic><topic>Temperature distribution</topic><topic>Thermal conductivity</topic><topic>Thermoelastic forced vibration</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhao, X.</creatorcontrib><creatorcontrib>Zhu, W.D.</creatorcontrib><creatorcontrib>Li, Y.H.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Journal of sound and vibration</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhao, X.</au><au>Zhu, W.D.</au><au>Li, Y.H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions</atitle><jtitle>Journal of sound and vibration</jtitle><date>2020-09-01</date><risdate>2020</risdate><volume>481</volume><spage>115407</spage><pages>115407-</pages><artnum>115407</artnum><issn>0022-460X</issn><eissn>1095-8568</eissn><abstract>Thermoelastic dynamic analysis of micro-/nano-beams is essential in the field of micro-/nano-electro-mechanical systems (MEMSs/NEMSs). However, the classical coupled thermoelastic theory is not suitable for the microscopic/nanoscopic case. As elementary parts of MEMSs/NEMSs, the size effect of micro-/nano-beams must be considered in their thermoelastic vibrations. This work originally explores analytical solutions of coupled thermoelastic forced vibrations of micro-/nano-beams based on Rayleigh beam theory and Eringen nonlocal elasticity theory. The heat conductivity equation is obtained by using the type Ⅲ Green-Naghdi theory. Coupled thermoelastic dynamic equations are decoupled by use of Green's function method and expressions of displacements, temperature fields, and thermal moments of micro-/nano-beams are derived. Furthermore, movement behaviors of an “ice core” of the temperature field are used to explain dynamic phenomena of the coupled system. Results from finite element analysis are compared with analytical solutions for verification purposes. This work primarily discusses influences of a small-scale parameter on coupled displacement and temperature fields and those of other important physical parameters, such as heating positions and height-to-length ratios of micro-/nano-beams, on system responses.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.jsv.2020.115407</doi></addata></record> |
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| ispartof | Journal of sound and vibration, 2020-09, Vol.481, p.115407, Article 115407 |
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| source | Elsevier ScienceDirect Journals |
| subjects | Beams (structural) Elasticity Exact solutions Finite element method Forced vibration Green's function Green's functions Green-Naghdi theory Heat conductivity Mathematical analysis Mechanical properties Mechanical systems Nonlocal elasticity Nonlocal elasticity theory Parameters Physical properties Size effects Temperature distribution Thermal conductivity Thermoelastic forced vibration Vibration |
| title | Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions |
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