Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method
In this paper the Fourier series method is introduced to obtain the solution for the displacement response of rectangular plates subjected to a blast loading. Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duffing type nonlinear ordinary differe...
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| Veröffentlicht in: | Computational mechanics 1999-02, Vol.23 (1), p.1-7 |
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| creator | TENG, T.-L LIANG, C.-C LIAO, C.-C |
| description | In this paper the Fourier series method is introduced to obtain the solution for the displacement response of rectangular plates subjected to a blast loading. Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duffing type nonlinear ordinary differential equations and then solved by adopting the Lindstedt-Poincar'e perturbation method. The complete analysis of square plates was carried out for all-clamped edge conditions. The results of deflection history and stress resultants which uses one perturbation term sufficiently correlated with results coming from both related literature as well as the finite element method. |
| doi_str_mv | 10.1007/s004660050380 |
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Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duffing type nonlinear ordinary differential equations and then solved by adopting the Lindstedt-Poincar'e perturbation method. The complete analysis of square plates was carried out for all-clamped edge conditions. The results of deflection history and stress resultants which uses one perturbation term sufficiently correlated with results coming from both related literature as well as the finite element method.</description><identifier>ISSN: 0178-7675</identifier><identifier>EISSN: 1432-0924</identifier><identifier>DOI: 10.1007/s004660050380</identifier><identifier>CODEN: CMMEEE</identifier><language>eng</language><publisher>Heidelberg: Springer</publisher><subject>Blast loads ; Exact sciences and technology ; Finite element method ; Forced vibration ; Fourier series ; Fundamental areas of phenomenology (including applications) ; Mathematical analysis ; Nonlinear analysis ; Nonlinear differential equations ; Nonlinear equations ; Ordinary differential equations ; Perturbation methods ; Physics ; Rectangular plates ; Resultants ; Solid mechanics ; Square plates ; Structural and continuum mechanics ; Vibration analysis ; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) ; Vibrations and mechanical waves</subject><ispartof>Computational mechanics, 1999-02, Vol.23 (1), p.1-7</ispartof><rights>1999 INIST-CNRS</rights><rights>Computational Mechanics is a copyright of Springer, (1999). 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Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duffing type nonlinear ordinary differential equations and then solved by adopting the Lindstedt-Poincar'e perturbation method. The complete analysis of square plates was carried out for all-clamped edge conditions. The results of deflection history and stress resultants which uses one perturbation term sufficiently correlated with results coming from both related literature as well as the finite element method.</description><subject>Blast loads</subject><subject>Exact sciences and technology</subject><subject>Finite element method</subject><subject>Forced vibration</subject><subject>Fourier series</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Mathematical analysis</subject><subject>Nonlinear analysis</subject><subject>Nonlinear differential equations</subject><subject>Nonlinear equations</subject><subject>Ordinary differential equations</subject><subject>Perturbation methods</subject><subject>Physics</subject><subject>Rectangular plates</subject><subject>Resultants</subject><subject>Solid mechanics</subject><subject>Square plates</subject><subject>Structural and continuum mechanics</subject><subject>Vibration analysis</subject><subject>Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)</subject><subject>Vibrations and mechanical waves</subject><issn>0178-7675</issn><issn>1432-0924</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpVkEFLAzEUhIMoWKtH7wG9rr5skk32KMWqUPSiFy9Lkn2xW7abmqRC_72rLYinOcw3wzCEXDK4YQDqNgGIqgKQwDUckQkTvCygLsUxmQBTulCVkqfkLKUVAJOaywl5fw5D3w1oIvUhOmzpV2ejyV0YqBlMv0tdosHTvEQa0WUzfGz7Ed70JmOidvfrzMM2dhhpwlESXWNehvacnHjTJ7w46JS8ze9fZ4_F4uXhaXa3KFxZl7mQwhrUgishWguGK4faWim111xb45VvhfZWgQHnFVaAsmW8drUEhNorPiVX-95NDJ9bTLlZjXPG7akpy4pJJkDASBV7ysWQUkTfbGK3NnHXMGh-7mv-3Tfy14dWk5zpfTSD69JfSAEDVvJv0PVvnQ</recordid><startdate>19990201</startdate><enddate>19990201</enddate><creator>TENG, T.-L</creator><creator>LIANG, C.-C</creator><creator>LIAO, C.-C</creator><general>Springer</general><general>Springer Nature B.V</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>19990201</creationdate><title>Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method</title><author>TENG, T.-L ; LIANG, C.-C ; LIAO, C.-C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c292t-54bae843744db0a37ce8bb558f838baf7fd48fb70a0cf7e60e5d139c950e09f73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Blast loads</topic><topic>Exact sciences and technology</topic><topic>Finite element method</topic><topic>Forced vibration</topic><topic>Fourier series</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Mathematical analysis</topic><topic>Nonlinear analysis</topic><topic>Nonlinear differential equations</topic><topic>Nonlinear equations</topic><topic>Ordinary differential equations</topic><topic>Perturbation methods</topic><topic>Physics</topic><topic>Rectangular plates</topic><topic>Resultants</topic><topic>Solid mechanics</topic><topic>Square plates</topic><topic>Structural and continuum mechanics</topic><topic>Vibration analysis</topic><topic>Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)</topic><topic>Vibrations and mechanical waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>TENG, T.-L</creatorcontrib><creatorcontrib>LIANG, C.-C</creatorcontrib><creatorcontrib>LIAO, C.-C</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Computational mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>TENG, T.-L</au><au>LIANG, C.-C</au><au>LIAO, C.-C</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method</atitle><jtitle>Computational mechanics</jtitle><date>1999-02-01</date><risdate>1999</risdate><volume>23</volume><issue>1</issue><spage>1</spage><epage>7</epage><pages>1-7</pages><issn>0178-7675</issn><eissn>1432-0924</eissn><coden>CMMEEE</coden><abstract>In this paper the Fourier series method is introduced to obtain the solution for the displacement response of rectangular plates subjected to a blast loading. Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duffing type nonlinear ordinary differential equations and then solved by adopting the Lindstedt-Poincar'e perturbation method. The complete analysis of square plates was carried out for all-clamped edge conditions. The results of deflection history and stress resultants which uses one perturbation term sufficiently correlated with results coming from both related literature as well as the finite element method.</abstract><cop>Heidelberg</cop><cop>Berlin</cop><pub>Springer</pub><doi>10.1007/s004660050380</doi><tpages>7</tpages></addata></record> |
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| ispartof | Computational mechanics, 1999-02, Vol.23 (1), p.1-7 |
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| source | SpringerNature Journals |
| subjects | Blast loads Exact sciences and technology Finite element method Forced vibration Fourier series Fundamental areas of phenomenology (including applications) Mathematical analysis Nonlinear analysis Nonlinear differential equations Nonlinear equations Ordinary differential equations Perturbation methods Physics Rectangular plates Resultants Solid mechanics Square plates Structural and continuum mechanics Vibration analysis Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Vibrations and mechanical waves |
| title | Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method |
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