On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation
The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system ar...
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Veröffentlicht in: | Journal of vibration and control 2019-03, Vol.25 (5), p.1058-1079 |
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description | The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. The results of perturbation analysis are in good agreement with results obtained from numerical methods. |
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K. A. ; Rofooei, F. R. ; Waezi, Z.</creator><creatorcontrib>Attari, N. K. A. ; Rofooei, F. R. ; Waezi, Z.</creatorcontrib><description>The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. The results of perturbation analysis are in good agreement with results obtained from numerical methods.</description><identifier>ISSN: 1077-5463</identifier><identifier>EISSN: 1741-2986</identifier><identifier>DOI: 10.1177/1077546318810072</identifier><language>eng</language><publisher>London, England: SAGE Publications</publisher><subject>Cylindrical tanks ; Differential equations ; Earthquakes ; Equations of motion ; Excitation ; Liquid sloshing ; Mathematical analysis ; Nonlinear analysis ; Nonlinear differential equations ; Nonlinear equations ; Numerical methods ; Perturbation methods ; Seismic activity ; Seismic engineering</subject><ispartof>Journal of vibration and control, 2019-03, Vol.25 (5), p.1058-1079</ispartof><rights>The Author(s) 2018</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c351t-d9782f78eb5bd8040b8975d707eb1c5480b90127e785bc041bcd1c5a02e62dda3</citedby><cites>FETCH-LOGICAL-c351t-d9782f78eb5bd8040b8975d707eb1c5480b90127e785bc041bcd1c5a02e62dda3</cites><orcidid>0000-0002-5490-078X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://journals.sagepub.com/doi/pdf/10.1177/1077546318810072$$EPDF$$P50$$Gsage$$H</linktopdf><linktohtml>$$Uhttps://journals.sagepub.com/doi/10.1177/1077546318810072$$EHTML$$P50$$Gsage$$H</linktohtml><link.rule.ids>315,782,786,21826,27931,27932,43628,43629</link.rule.ids></links><search><creatorcontrib>Attari, N. K. A.</creatorcontrib><creatorcontrib>Rofooei, F. R.</creatorcontrib><creatorcontrib>Waezi, Z.</creatorcontrib><title>On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation</title><title>Journal of vibration and control</title><description>The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. The results of perturbation analysis are in good agreement with results obtained from numerical methods.</description><subject>Cylindrical tanks</subject><subject>Differential equations</subject><subject>Earthquakes</subject><subject>Equations of motion</subject><subject>Excitation</subject><subject>Liquid sloshing</subject><subject>Mathematical analysis</subject><subject>Nonlinear analysis</subject><subject>Nonlinear differential equations</subject><subject>Nonlinear equations</subject><subject>Numerical methods</subject><subject>Perturbation methods</subject><subject>Seismic activity</subject><subject>Seismic engineering</subject><issn>1077-5463</issn><issn>1741-2986</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1UEtLAzEQDqJgrd49BjyvTrZJkz1K8QWFXvS85LU1dU3aJAuuv97UCoIgDMzwvWA-hC4JXBPC-Q0Bzhmdz4gQBIDXR2hCOCVV3Yj5cbkLXe35U3SW0gYAKCUwQePKYx9877yVEW9tzENUMrvgsfSyH5NLOHRY4pTjoAtpsZYxjs6vC6hd1ENfjHosCSY6LXvcu93gDM7Sv-HBGxvxa4juM_hcSPuhXf7OP0cnneyTvfjZU_Ryf_e8eKyWq4enxe2y0jNGcmUaLuqOC6uYMgIoKNFwZjhwq4hmVIBqgNTccsGUBkqUNgWXUNt5bYycTdHVIXcbw26wKbebMMTyW2prwgljtExRwUGlY0gp2q7dRvcu49gSaPcFt38LLpbqYElybX9D_9V_AWqffQg</recordid><startdate>201903</startdate><enddate>201903</enddate><creator>Attari, N. K. A.</creator><creator>Rofooei, F. R.</creator><creator>Waezi, Z.</creator><general>SAGE Publications</general><general>SAGE PUBLICATIONS, INC</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-5490-078X</orcidid></search><sort><creationdate>201903</creationdate><title>On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation</title><author>Attari, N. K. A. ; Rofooei, F. R. ; Waezi, Z.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c351t-d9782f78eb5bd8040b8975d707eb1c5480b90127e785bc041bcd1c5a02e62dda3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Cylindrical tanks</topic><topic>Differential equations</topic><topic>Earthquakes</topic><topic>Equations of motion</topic><topic>Excitation</topic><topic>Liquid sloshing</topic><topic>Mathematical analysis</topic><topic>Nonlinear analysis</topic><topic>Nonlinear differential equations</topic><topic>Nonlinear equations</topic><topic>Numerical methods</topic><topic>Perturbation methods</topic><topic>Seismic activity</topic><topic>Seismic engineering</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Attari, N. K. A.</creatorcontrib><creatorcontrib>Rofooei, F. R.</creatorcontrib><creatorcontrib>Waezi, Z.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>Journal of vibration and control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Attari, N. K. A.</au><au>Rofooei, F. R.</au><au>Waezi, Z.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation</atitle><jtitle>Journal of vibration and control</jtitle><date>2019-03</date><risdate>2019</risdate><volume>25</volume><issue>5</issue><spage>1058</spage><epage>1079</epage><pages>1058-1079</pages><issn>1077-5463</issn><eissn>1741-2986</eissn><abstract>The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode response with respect to the excitation amplitude. The saturation phenomenon is observed in the decoupled modes of the system; however, the structural mode and the first anti-symmetric mode of liquid are a combination of the saturated mode and another mode whose scale factor is crucial for the structural response. The results of perturbation analysis are in good agreement with results obtained from numerical methods.</abstract><cop>London, England</cop><pub>SAGE Publications</pub><doi>10.1177/1077546318810072</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0002-5490-078X</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Cylindrical tanks Differential equations Earthquakes Equations of motion Excitation Liquid sloshing Mathematical analysis Nonlinear analysis Nonlinear differential equations Nonlinear equations Numerical methods Perturbation methods Seismic activity Seismic engineering |
title | On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation |
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