Fundamental frequency analysis of laminated rectangular plates by differential quadrature method
In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polyno...
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Veröffentlicht in: | International journal for numerical methods in engineering 1993-07, Vol.36 (14), p.2341-2356 |
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creator | Farsa, Jalaleddin Kukreti, Anant R. Bert, Charles W. |
description | In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross‐ply, and symmetric, balanced angle‐ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time. |
doi_str_mv | 10.1002/nme.1620361403 |
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The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross‐ply, and symmetric, balanced angle‐ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time.</description><identifier>ISSN: 0029-5981</identifier><identifier>EISSN: 1097-0207</identifier><identifier>DOI: 10.1002/nme.1620361403</identifier><identifier>CODEN: IJNMBH</identifier><language>eng</language><publisher>New York: John Wiley & Sons, Ltd</publisher><subject>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>International journal for numerical methods in engineering, 1993-07, Vol.36 (14), p.2341-2356</ispartof><rights>Copyright © 1993 John Wiley & Sons, Ltd</rights><rights>1993 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4163-3221516a0ae6427fa7b5e7233710fac69f1d6a094b083a78bc4efd73001926373</citedby><cites>FETCH-LOGICAL-c4163-3221516a0ae6427fa7b5e7233710fac69f1d6a094b083a78bc4efd73001926373</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnme.1620361403$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnme.1620361403$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=4796841$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Farsa, Jalaleddin</creatorcontrib><creatorcontrib>Kukreti, Anant R.</creatorcontrib><creatorcontrib>Bert, Charles W.</creatorcontrib><title>Fundamental frequency analysis of laminated rectangular plates by differential quadrature method</title><title>International journal for numerical methods in engineering</title><addtitle>Int. J. Numer. Meth. Engng</addtitle><description>In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross‐ply, and symmetric, balanced angle‐ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time.</description><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>0029-5981</issn><issn>1097-0207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1993</creationdate><recordtype>article</recordtype><recordid>eNqNkM1v1DAQxS1EJZYtV84-IG7Z-iOx4yMqbam0FAmB2puZTcZgcJytnajkv8fVVkWcinywZL_3m3mPkNecbThj4iQOuOFKMKl4zeQzsuLM6IoJpp-TVRGYqjEtf0Fe5vyTMc4bJlfk2_kcexgwThCoS3g7Y-wWChHCkn2mo6MBBh9hwp4m7CaI3-cAie5Decp0t9DeO4epEHxB3M7QJ5jmhHTA6cfYH5MjByHjq4d7Tb6en305_VBtP11cnr7bVl3NlaykELzhChigqoV2oHcNaiGl5sxBp4zjffk19Y61EnS762p0vZYliBFKarkmbw_cfRpLiDzZwecOQ4CI45ytUExKXs5_CIVpS4NrsjkIuzTmnNDZffIDpMVyZu8bt6Vx-7fxYnjzQIbcQXAJYufzo6vWRrX1_QLmILvzAZcnoPbq49k_I6qD1-cJfz96If2ySkvd2OurC3vTyO3n982NvZZ_ALjXoRs</recordid><startdate>19930730</startdate><enddate>19930730</enddate><creator>Farsa, Jalaleddin</creator><creator>Kukreti, Anant R.</creator><creator>Bert, Charles W.</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7SM</scope><scope>7SR</scope><scope>FR3</scope><scope>JG9</scope></search><sort><creationdate>19930730</creationdate><title>Fundamental frequency analysis of laminated rectangular plates by differential quadrature method</title><author>Farsa, Jalaleddin ; Kukreti, Anant R. ; Bert, Charles W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4163-3221516a0ae6427fa7b5e7233710fac69f1d6a094b083a78bc4efd73001926373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1993</creationdate><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>Farsa, Jalaleddin</creatorcontrib><creatorcontrib>Kukreti, Anant R.</creatorcontrib><creatorcontrib>Bert, Charles W.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Earthquake Engineering Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><jtitle>International journal for numerical methods in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Farsa, Jalaleddin</au><au>Kukreti, Anant R.</au><au>Bert, Charles W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fundamental frequency analysis of laminated rectangular plates by differential quadrature method</atitle><jtitle>International journal for numerical methods in engineering</jtitle><addtitle>Int. J. Numer. Meth. Engng</addtitle><date>1993-07-30</date><risdate>1993</risdate><volume>36</volume><issue>14</issue><spage>2341</spage><epage>2356</epage><pages>2341-2356</pages><issn>0029-5981</issn><eissn>1097-0207</eissn><coden>IJNMBH</coden><abstract>In this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross‐ply, and symmetric, balanced angle‐ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time.</abstract><cop>New York</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/nme.1620361403</doi><tpages>16</tpages></addata></record> |
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subjects | 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 | Fundamental frequency analysis of laminated rectangular plates by differential quadrature method |
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