Dynamic analysis of size-dependent micro-beams with nonlinear elasticity under electrical actuation
This paper presents a nonlinear electro-dynamic analysis for a size dependent micro-beam made of materials with nonlinear elasticity by employing the modified couple stress theory based on Euler-Bernoulli beam model. By employing Hamilton's principle, the nonlinear partial differential governin...
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| Veröffentlicht in: | Applied Mathematical Modelling 2017-03, Vol.43, p.441-453 |
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| creator | Peng, Jianshe Yang, Liu Lin, Fan Yang, Jie |
| description | This paper presents a nonlinear electro-dynamic analysis for a size dependent micro-beam made of materials with nonlinear elasticity by employing the modified couple stress theory based on Euler-Bernoulli beam model. By employing Hamilton's principle, the nonlinear partial differential governing equation is derived then solved by using Galerkin method in the space domain and backward differential method in the time domain to obtain the nonlinear electro-dynamic response and phase portrait of the micro-beam. A parametric study is conducted, with a particular focus on the influences of nonlinear elasticity and size-dependency of the micro-beam on its nonlinear dynamic behavior. Numerical results show that a micro-beam exhibiting nonlinear elastic stress-strain relationship has reduced effective stiffness while the size effect has the opposite effect. |
| doi_str_mv | 10.1016/j.apm.2016.11.025 |
| format | Article |
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By employing Hamilton's principle, the nonlinear partial differential governing equation is derived then solved by using Galerkin method in the space domain and backward differential method in the time domain to obtain the nonlinear electro-dynamic response and phase portrait of the micro-beam. A parametric study is conducted, with a particular focus on the influences of nonlinear elasticity and size-dependency of the micro-beam on its nonlinear dynamic behavior. Numerical results show that a micro-beam exhibiting nonlinear elastic stress-strain relationship has reduced effective stiffness while the size effect has the opposite effect.</description><identifier>ISSN: 0307-904X</identifier><identifier>ISSN: 1088-8691</identifier><identifier>EISSN: 0307-904X</identifier><identifier>DOI: 10.1016/j.apm.2016.11.025</identifier><language>eng</language><publisher>New York: Elsevier BV</publisher><subject>Actuation ; Differential equations ; Dynamic response ; Elasticity ; Euler-Bernoulli beams ; Galerkin method ; Hamilton's principle ; Materials elasticity ; Mathematical models ; Microbeams ; Microelectromechanical systems ; Nonlinear analysis ; Nonlinear equations ; Nonlinear response ; Partial differential equations ; Size effects ; Stiffness ; Strain ; Stress-strain relationships ; Time domain analysis</subject><ispartof>Applied Mathematical Modelling, 2017-03, Vol.43, p.441-453</ispartof><rights>Copyright Elsevier BV Mar 2017</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-171de402232a80434219e3a9618c7755f0eca303bc9f8a8f2b7417d1132b44403</citedby><cites>FETCH-LOGICAL-c316t-171de402232a80434219e3a9618c7755f0eca303bc9f8a8f2b7417d1132b44403</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Peng, Jianshe</creatorcontrib><creatorcontrib>Yang, Liu</creatorcontrib><creatorcontrib>Lin, Fan</creatorcontrib><creatorcontrib>Yang, Jie</creatorcontrib><title>Dynamic analysis of size-dependent micro-beams with nonlinear elasticity under electrical actuation</title><title>Applied Mathematical Modelling</title><description>This paper presents a nonlinear electro-dynamic analysis for a size dependent micro-beam made of materials with nonlinear elasticity by employing the modified couple stress theory based on Euler-Bernoulli beam model. By employing Hamilton's principle, the nonlinear partial differential governing equation is derived then solved by using Galerkin method in the space domain and backward differential method in the time domain to obtain the nonlinear electro-dynamic response and phase portrait of the micro-beam. A parametric study is conducted, with a particular focus on the influences of nonlinear elasticity and size-dependency of the micro-beam on its nonlinear dynamic behavior. Numerical results show that a micro-beam exhibiting nonlinear elastic stress-strain relationship has reduced effective stiffness while the size effect has the opposite effect.</description><subject>Actuation</subject><subject>Differential equations</subject><subject>Dynamic response</subject><subject>Elasticity</subject><subject>Euler-Bernoulli beams</subject><subject>Galerkin method</subject><subject>Hamilton's principle</subject><subject>Materials elasticity</subject><subject>Mathematical models</subject><subject>Microbeams</subject><subject>Microelectromechanical systems</subject><subject>Nonlinear analysis</subject><subject>Nonlinear equations</subject><subject>Nonlinear response</subject><subject>Partial differential equations</subject><subject>Size effects</subject><subject>Stiffness</subject><subject>Strain</subject><subject>Stress-strain relationships</subject><subject>Time domain analysis</subject><issn>0307-904X</issn><issn>1088-8691</issn><issn>0307-904X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNpNkEtLBDEQhIMouK7-AG8BzzN2J5nXUdYnLHhR8BYymQxmmJdJBhl_vVnWg6euri4a6iPkGiFFwPy2S9U8pCzKFDEFlp2QDXAokgrEx-k_fU4uvO8AIIvbhuj7dVSD1VSNql-99XRqqbc_JmnMbMbGjIHGs5uS2qjB028bPuk4jb0djXLU9MoHq21Y6RLDB8Po4KxWPVU6LCrYabwkZ63qvbn6m1vy_vjwtntO9q9PL7u7faI55iHBAhsjgDHOVAmCC4aV4arKsdRFkWUtGK048FpXbanKltWFwKJB5KwWQgDfkpvj39lNX4vxQXbT4mIvL7HiDBkUIo8pPKZiKe-daeXs7KDcKhHkgaXsZGQpDywloows-S8uPWjj</recordid><startdate>201703</startdate><enddate>201703</enddate><creator>Peng, Jianshe</creator><creator>Yang, Liu</creator><creator>Lin, Fan</creator><creator>Yang, Jie</creator><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201703</creationdate><title>Dynamic analysis of size-dependent micro-beams with nonlinear elasticity under electrical actuation</title><author>Peng, Jianshe ; Yang, Liu ; Lin, Fan ; Yang, Jie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-171de402232a80434219e3a9618c7755f0eca303bc9f8a8f2b7417d1132b44403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Actuation</topic><topic>Differential equations</topic><topic>Dynamic response</topic><topic>Elasticity</topic><topic>Euler-Bernoulli beams</topic><topic>Galerkin method</topic><topic>Hamilton's principle</topic><topic>Materials elasticity</topic><topic>Mathematical models</topic><topic>Microbeams</topic><topic>Microelectromechanical systems</topic><topic>Nonlinear analysis</topic><topic>Nonlinear equations</topic><topic>Nonlinear response</topic><topic>Partial differential equations</topic><topic>Size effects</topic><topic>Stiffness</topic><topic>Strain</topic><topic>Stress-strain relationships</topic><topic>Time domain analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Peng, Jianshe</creatorcontrib><creatorcontrib>Yang, Liu</creatorcontrib><creatorcontrib>Lin, Fan</creatorcontrib><creatorcontrib>Yang, Jie</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied Mathematical Modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Peng, Jianshe</au><au>Yang, Liu</au><au>Lin, Fan</au><au>Yang, Jie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamic analysis of size-dependent micro-beams with nonlinear elasticity under electrical actuation</atitle><jtitle>Applied Mathematical Modelling</jtitle><date>2017-03</date><risdate>2017</risdate><volume>43</volume><spage>441</spage><epage>453</epage><pages>441-453</pages><issn>0307-904X</issn><issn>1088-8691</issn><eissn>0307-904X</eissn><abstract>This paper presents a nonlinear electro-dynamic analysis for a size dependent micro-beam made of materials with nonlinear elasticity by employing the modified couple stress theory based on Euler-Bernoulli beam model. By employing Hamilton's principle, the nonlinear partial differential governing equation is derived then solved by using Galerkin method in the space domain and backward differential method in the time domain to obtain the nonlinear electro-dynamic response and phase portrait of the micro-beam. A parametric study is conducted, with a particular focus on the influences of nonlinear elasticity and size-dependency of the micro-beam on its nonlinear dynamic behavior. Numerical results show that a micro-beam exhibiting nonlinear elastic stress-strain relationship has reduced effective stiffness while the size effect has the opposite effect.</abstract><cop>New York</cop><pub>Elsevier BV</pub><doi>10.1016/j.apm.2016.11.025</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Applied Mathematical Modelling, 2017-03, Vol.43, p.441-453 |
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| source | Elsevier ScienceDirect Journals Complete; EBSCOhost Business Source Complete; EZB-FREE-00999 freely available EZB journals; EBSCOhost Education Source |
| subjects | Actuation Differential equations Dynamic response Elasticity Euler-Bernoulli beams Galerkin method Hamilton's principle Materials elasticity Mathematical models Microbeams Microelectromechanical systems Nonlinear analysis Nonlinear equations Nonlinear response Partial differential equations Size effects Stiffness Strain Stress-strain relationships Time domain analysis |
| title | Dynamic analysis of size-dependent micro-beams with nonlinear elasticity under electrical actuation |
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