Nonlinear vibrations of a composite circular plate with a rigid body
The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamil...
Gespeichert in:
| Veröffentlicht in: | Applied mathematics and mechanics 2023-06, Vol.44 (6), p.857-876 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 876 |
|---|---|
| container_issue | 6 |
| container_start_page | 857 |
| container_title | Applied mathematics and mechanics |
| container_volume | 44 |
| creator | Meng, Ying Mao, Xiaoye Ding, Hu Chen, Liqun |
| description | The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton’s principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical. |
| doi_str_mv | 10.1007/s10483-023-3005-8 |
| format | Article |
| fullrecord | <record><control><sourceid>wanfang_jour_proqu</sourceid><recordid>TN_cdi_wanfang_journals_yysxhlx_e202306001</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><wanfj_id>yysxhlx_e202306001</wanfj_id><sourcerecordid>yysxhlx_e202306001</sourcerecordid><originalsourceid>FETCH-LOGICAL-c352t-a6ec9c90b43c5c560eb7c48c1cad7f3f903f38ec8260a1008f0b1cd86b5591f13</originalsourceid><addsrcrecordid>eNpFkE1LAzEQhoMoWKs_wNuCN2F18rXJHqV-QtGLnkM2m7Qp62ZNtrb996ZU6Gl4mYd3mAehawx3GEDcJwxM0hIILSkAL-UJmmAuaEkEZ6doAoTTkkkiztFFSisAYIKxCXp8D33ne6tj8eubqEcf-lQEV-jChO8hJD_awvho1l1Ghk7nuPHjMu-jX_i2aEK7u0RnTnfJXv3PKfp6fvqcvZbzj5e32cO8NJSTsdSVNbWpoWHUcMMrsI0wTBpsdCscdTVQR6U1klSg81fSQYNNK6uG8xo7TKfo9tC70b3T_UKtwjr2-aLa7dJ22W2VJdkAVAB7-OYADzH8rG0ajzSRJNfXlIlMkQOVhuj7hY1HCoPaq1UHtSoXq71aJekfe0Rreg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2821009347</pqid></control><display><type>article</type><title>Nonlinear vibrations of a composite circular plate with a rigid body</title><source>Alma/SFX Local Collection</source><source>SpringerLink Journals - AutoHoldings</source><creator>Meng, Ying ; Mao, Xiaoye ; Ding, Hu ; Chen, Liqun</creator><creatorcontrib>Meng, Ying ; Mao, Xiaoye ; Ding, Hu ; Chen, Liqun</creatorcontrib><description>The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton’s principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical.</description><edition>English ed.</edition><identifier>ISSN: 0253-4827</identifier><identifier>EISSN: 1573-2754</identifier><identifier>DOI: 10.1007/s10483-023-3005-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Circular plates ; Classical Mechanics ; Configurations ; Dynamic models ; Finite element method ; Fluid- and Aerodynamics ; Forced vibration ; Hamilton's principle ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Plate theory ; Resonant frequencies ; Rigid structures ; Vibration response</subject><ispartof>Applied mathematics and mechanics, 2023-06, Vol.44 (6), p.857-876</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>Copyright © Wanfang Data Co. Ltd. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c352t-a6ec9c90b43c5c560eb7c48c1cad7f3f903f38ec8260a1008f0b1cd86b5591f13</citedby><cites>FETCH-LOGICAL-c352t-a6ec9c90b43c5c560eb7c48c1cad7f3f903f38ec8260a1008f0b1cd86b5591f13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://www.wanfangdata.com.cn/images/PeriodicalImages/yysxhlx-e/yysxhlx-e.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10483-023-3005-8$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10483-023-3005-8$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Meng, Ying</creatorcontrib><creatorcontrib>Mao, Xiaoye</creatorcontrib><creatorcontrib>Ding, Hu</creatorcontrib><creatorcontrib>Chen, Liqun</creatorcontrib><title>Nonlinear vibrations of a composite circular plate with a rigid body</title><title>Applied mathematics and mechanics</title><addtitle>Appl. Math. Mech.-Engl. Ed</addtitle><description>The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton’s principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical.</description><subject>Applications of Mathematics</subject><subject>Circular plates</subject><subject>Classical Mechanics</subject><subject>Configurations</subject><subject>Dynamic models</subject><subject>Finite element method</subject><subject>Fluid- and Aerodynamics</subject><subject>Forced vibration</subject><subject>Hamilton's principle</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Plate theory</subject><subject>Resonant frequencies</subject><subject>Rigid structures</subject><subject>Vibration response</subject><issn>0253-4827</issn><issn>1573-2754</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNpFkE1LAzEQhoMoWKs_wNuCN2F18rXJHqV-QtGLnkM2m7Qp62ZNtrb996ZU6Gl4mYd3mAehawx3GEDcJwxM0hIILSkAL-UJmmAuaEkEZ6doAoTTkkkiztFFSisAYIKxCXp8D33ne6tj8eubqEcf-lQEV-jChO8hJD_awvho1l1Ghk7nuPHjMu-jX_i2aEK7u0RnTnfJXv3PKfp6fvqcvZbzj5e32cO8NJSTsdSVNbWpoWHUcMMrsI0wTBpsdCscdTVQR6U1klSg81fSQYNNK6uG8xo7TKfo9tC70b3T_UKtwjr2-aLa7dJ22W2VJdkAVAB7-OYADzH8rG0ajzSRJNfXlIlMkQOVhuj7hY1HCoPaq1UHtSoXq71aJekfe0Rreg</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Meng, Ying</creator><creator>Mao, Xiaoye</creator><creator>Ding, Hu</creator><creator>Chen, Liqun</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>Shanghai Institute of Applied Mathematics and Mechanics,School of Mechanics and Engineering Science,Shanghai University,Shanghai 200444,China</general><scope>C6C</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20230601</creationdate><title>Nonlinear vibrations of a composite circular plate with a rigid body</title><author>Meng, Ying ; Mao, Xiaoye ; Ding, Hu ; Chen, Liqun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c352t-a6ec9c90b43c5c560eb7c48c1cad7f3f903f38ec8260a1008f0b1cd86b5591f13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Circular plates</topic><topic>Classical Mechanics</topic><topic>Configurations</topic><topic>Dynamic models</topic><topic>Finite element method</topic><topic>Fluid- and Aerodynamics</topic><topic>Forced vibration</topic><topic>Hamilton's principle</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Plate theory</topic><topic>Resonant frequencies</topic><topic>Rigid structures</topic><topic>Vibration response</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Meng, Ying</creatorcontrib><creatorcontrib>Mao, Xiaoye</creatorcontrib><creatorcontrib>Ding, Hu</creatorcontrib><creatorcontrib>Chen, Liqun</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Applied mathematics and mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Meng, Ying</au><au>Mao, Xiaoye</au><au>Ding, Hu</au><au>Chen, Liqun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonlinear vibrations of a composite circular plate with a rigid body</atitle><jtitle>Applied mathematics and mechanics</jtitle><stitle>Appl. Math. Mech.-Engl. Ed</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>44</volume><issue>6</issue><spage>857</spage><epage>876</epage><pages>857-876</pages><issn>0253-4827</issn><eissn>1573-2754</eissn><abstract>The influence of weights is usually ignored in the study of nonlinear vibrations of plates. In this paper, the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented. The nonlinear governing equations are derived from the generalized Hamilton’s principle and the von Kármán plate theory. The equilibrium configurations due to weights are determined and validated by the finite element method (FEM). A nonlinear model for the vibration around the equilibrium configuration is established. Moreover, the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated. The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model. This leads to interesting phenomena. For example, considering weights increases the natural frequency. Furthermore, when the influence of weights is considered, the vibration response of the plate becomes asymmetrical.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s10483-023-3005-8</doi><tpages>20</tpages><edition>English ed.</edition><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0253-4827 |
| ispartof | Applied mathematics and mechanics, 2023-06, Vol.44 (6), p.857-876 |
| issn | 0253-4827 1573-2754 |
| language | eng |
| recordid | cdi_wanfang_journals_yysxhlx_e202306001 |
| source | Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Circular plates Classical Mechanics Configurations Dynamic models Finite element method Fluid- and Aerodynamics Forced vibration Hamilton's principle Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Partial Differential Equations Plate theory Resonant frequencies Rigid structures Vibration response |
| title | Nonlinear vibrations of a composite circular plate with a rigid body |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T19%3A23%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wanfang_jour_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Nonlinear%20vibrations%20of%20a%20composite%20circular%20plate%20with%20a%20rigid%20body&rft.jtitle=Applied%20mathematics%20and%20mechanics&rft.au=Meng,%20Ying&rft.date=2023-06-01&rft.volume=44&rft.issue=6&rft.spage=857&rft.epage=876&rft.pages=857-876&rft.issn=0253-4827&rft.eissn=1573-2754&rft_id=info:doi/10.1007/s10483-023-3005-8&rft_dat=%3Cwanfang_jour_proqu%3Eyysxhlx_e202306001%3C/wanfang_jour_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2821009347&rft_id=info:pmid/&rft_wanfj_id=yysxhlx_e202306001&rfr_iscdi=true |