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New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators
Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analyti...
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description | Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions. |
doi_str_mv | 10.1063/1.4952117 |
format | conference_proceeding |
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M. Fatih ; Pakdemirli, Mehmet</creator><contributor>Simos, Theodore ; Tsitouras, Charalambos</contributor><creatorcontrib>Karahan, M. M. Fatih ; Pakdemirli, Mehmet ; Simos, Theodore ; Tsitouras, Charalambos</creatorcontrib><description>Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.</description><identifier>ISSN: 0094-243X</identifier><identifier>EISSN: 1551-7616</identifier><identifier>DOI: 10.1063/1.4952117</identifier><identifier>CODEN: APCPCS</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Computer simulation ; Duffing oscillators ; Frequency response ; Oscillators</subject><ispartof>AIP Conference Proceedings, 2016, Vol.1738 (1)</ispartof><rights>Author(s)</rights><rights>2016 Author(s). Published by AIP Publishing.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>310,311,315,786,790,795,796,23958,23959,25170,27957,27958</link.rule.ids></links><search><contributor>Simos, Theodore</contributor><contributor>Tsitouras, Charalambos</contributor><creatorcontrib>Karahan, M. M. Fatih</creatorcontrib><creatorcontrib>Pakdemirli, Mehmet</creatorcontrib><title>New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators</title><title>AIP Conference Proceedings</title><description>Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.</description><subject>Computer simulation</subject><subject>Duffing oscillators</subject><subject>Frequency response</subject><subject>Oscillators</subject><issn>0094-243X</issn><issn>1551-7616</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2016</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNp9kMtKAzEUhoMoWKsL3yDgTpiak2QmM0sp3qDoRsVdyKRJTRmTaZJR-_ZOseDO1YHDdy7fj9A5kBmQil3BjDclBRAHaAJlCYWooDpEE0IaXlDO3o7RSUprQmgjRD1Br4_mC6u-j-HbfahscArdkF3wCdsQcX4fOzkGv-q22AffOW9UxHponS42g_PZabwcrHV-hUPSrutUDjGdoiOrumTO9nWKXm5vnuf3xeLp7mF-vSh6WrJcmLrWujUKagONospapk2lBGNVKUS5JFDRJeeEtzVvQShOtFXajjKqpKRu2RRd_O4dBTaDSVmuwxD9eFJSoCC44BUZqctfanwwq52d7OOoG7fyM0QJcp-Z7Jf2PxiI3IX8N8B-APO5b90</recordid><startdate>20160608</startdate><enddate>20160608</enddate><creator>Karahan, M. M. Fatih</creator><creator>Pakdemirli, Mehmet</creator><general>American Institute of Physics</general><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20160608</creationdate><title>New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators</title><author>Karahan, M. M. Fatih ; Pakdemirli, Mehmet</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p253t-e88ccbea18e19a2aff3ce6a73365775d0162d4404b84b17a40cfacf009a5208b3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Computer simulation</topic><topic>Duffing oscillators</topic><topic>Frequency response</topic><topic>Oscillators</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Karahan, M. M. Fatih</creatorcontrib><creatorcontrib>Pakdemirli, Mehmet</creatorcontrib><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Karahan, M. M. Fatih</au><au>Pakdemirli, Mehmet</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators</atitle><btitle>AIP Conference Proceedings</btitle><date>2016-06-08</date><risdate>2016</risdate><volume>1738</volume><issue>1</issue><issn>0094-243X</issn><eissn>1551-7616</eissn><coden>APCPCS</coden><abstract>Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.4952117</doi><tpages>4</tpages></addata></record> |
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source | American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list) |
subjects | Computer simulation Duffing oscillators Frequency response Oscillators |
title | New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators |
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