Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method
This paper presents the exact static and dynamic analyses of simply supported rectangular plates. The analytical solutions for displacements, buckling loads, natural frequencies and dynamic responses are obtained by using the double U-transformation method and the finite difference method. After an...
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| Veröffentlicht in: | Journal of sound and vibration 2006-01, Vol.289 (1), p.66-76 |
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| container_end_page | 76 |
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| container_title | Journal of sound and vibration |
| container_volume | 289 |
| creator | Liu, J.K. Yang, Y. Cai, C.W. |
| description | This paper presents the exact static and dynamic analyses of simply supported rectangular plates. The analytical solutions for displacements, buckling loads, natural frequencies and dynamic responses are obtained by using the double U-transformation method and the finite difference method. After an equivalent system with cyclic periodicity in two directions is established, the difference governing equation for such an equivalent system can be uncoupled by applying the double U-transformation. Then the exact analytical finite difference solutions, the exact error expressions and the exact convergence rates are derived. These results cannot be obtained if other methods are used instead. |
| doi_str_mv | 10.1016/j.jsv.2005.01.036 |
| format | Article |
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The analytical solutions for displacements, buckling loads, natural frequencies and dynamic responses are obtained by using the double U-transformation method and the finite difference method. After an equivalent system with cyclic periodicity in two directions is established, the difference governing equation for such an equivalent system can be uncoupled by applying the double U-transformation. Then the exact analytical finite difference solutions, the exact error expressions and the exact convergence rates are derived. These results cannot be obtained if other methods are used instead.</description><identifier>ISSN: 0022-460X</identifier><identifier>EISSN: 1095-8568</identifier><identifier>DOI: 10.1016/j.jsv.2005.01.036</identifier><identifier>CODEN: JSVIAG</identifier><language>eng</language><publisher>London: Elsevier Ltd</publisher><subject>Buckling ; Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Physics ; Solid mechanics ; Structural and continuum mechanics ; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)</subject><ispartof>Journal of sound and vibration, 2006-01, Vol.289 (1), p.66-76</ispartof><rights>2005 Elsevier Ltd</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-4c27470d59ed45938935c62f4a5e51805e002073c63e8ec565925817c37ec4093</citedby><cites>FETCH-LOGICAL-c358t-4c27470d59ed45938935c62f4a5e51805e002073c63e8ec565925817c37ec4093</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.2005.01.036$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17245110$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, J.K.</creatorcontrib><creatorcontrib>Yang, Y.</creatorcontrib><creatorcontrib>Cai, C.W.</creatorcontrib><title>Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method</title><title>Journal of sound and vibration</title><description>This paper presents the exact static and dynamic analyses of simply supported rectangular plates. The analytical solutions for displacements, buckling loads, natural frequencies and dynamic responses are obtained by using the double U-transformation method and the finite difference method. After an equivalent system with cyclic periodicity in two directions is established, the difference governing equation for such an equivalent system can be uncoupled by applying the double U-transformation. Then the exact analytical finite difference solutions, the exact error expressions and the exact convergence rates are derived. These results cannot be obtained if other methods are used instead.</description><subject>Buckling</subject><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Physics</subject><subject>Solid mechanics</subject><subject>Structural and continuum mechanics</subject><subject>Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)</subject><issn>0022-460X</issn><issn>1095-8568</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp9kEtrHDEQhEWIIRsnPyA3XZLbjFuveZBTWOIkYMglBt-ELLVsLTOajaRdWPLnrfEacvOpC7qqmv4I-cSgZcC6q127y8eWA6gWWAuie0M2DEbVDKob3pINAOeN7ODuHXmf8w4ARinkhvzbLvGI6QGjRZrLwQXMdIlVmhIsNdFRd4pmftZmOuV17el-MqWq-xM95BAfaHlEetuUZGL2S5prtnas4XXhQwwFqQveY3o-NGN5XNwHcuHNlPHjy7wkt9ff_2x_Nje_f_zafrtprFBDaaTlvezBqRGdVKMYRqFsx700ChUbQGF9DnphO4EDWtWpkauB9Vb0aCWM4pJ8Offu0_L3gLnoOWSL02QiLoes-cgU63hfjexstGnJOaHX-xRmk06agV4x652umPWKWQPTFXPNfH4pN9mayVcENuT_wZ5LxRhU39ezD-unx4BJZxtWGC4ktEW7Jbxy5Qk4iJNL</recordid><startdate>20060101</startdate><enddate>20060101</enddate><creator>Liu, J.K.</creator><creator>Yang, Y.</creator><creator>Cai, C.W.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope></search><sort><creationdate>20060101</creationdate><title>Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method</title><author>Liu, J.K. ; Yang, Y. ; Cai, C.W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-4c27470d59ed45938935c62f4a5e51805e002073c63e8ec565925817c37ec4093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Buckling</topic><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Physics</topic><topic>Solid mechanics</topic><topic>Structural and continuum mechanics</topic><topic>Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, J.K.</creatorcontrib><creatorcontrib>Yang, Y.</creatorcontrib><creatorcontrib>Cai, C.W.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><jtitle>Journal of sound and vibration</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, J.K.</au><au>Yang, Y.</au><au>Cai, C.W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method</atitle><jtitle>Journal of sound and vibration</jtitle><date>2006-01-01</date><risdate>2006</risdate><volume>289</volume><issue>1</issue><spage>66</spage><epage>76</epage><pages>66-76</pages><issn>0022-460X</issn><eissn>1095-8568</eissn><coden>JSVIAG</coden><abstract>This paper presents the exact static and dynamic analyses of simply supported rectangular plates. The analytical solutions for displacements, buckling loads, natural frequencies and dynamic responses are obtained by using the double U-transformation method and the finite difference method. After an equivalent system with cyclic periodicity in two directions is established, the difference governing equation for such an equivalent system can be uncoupled by applying the double U-transformation. Then the exact analytical finite difference solutions, the exact error expressions and the exact convergence rates are derived. These results cannot be obtained if other methods are used instead.</abstract><cop>London</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.jsv.2005.01.036</doi><tpages>11</tpages></addata></record> |
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| subjects | Buckling Exact sciences and technology Fundamental areas of phenomenology (including applications) Physics Solid mechanics Structural and continuum mechanics Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) |
| title | Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method |
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