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A new analytical technique to find periodic solutions of non-linear systems
Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for [ x ( 0 ) = a 0 , x ˙ ( 0...
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| Published in: | International journal of non-linear mechanics 2007-10, Vol.42 (8), p.1035-1045 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c352t-124e6e15b493febd0b506fefc2bc5fd351952b635d1b6598629c429beda523853 |
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| cites | cdi_FETCH-LOGICAL-c352t-124e6e15b493febd0b506fefc2bc5fd351952b635d1b6598629c429beda523853 |
| container_end_page | 1045 |
| container_issue | 8 |
| container_start_page | 1035 |
| container_title | International journal of non-linear mechanics |
| container_volume | 42 |
| creator | Alam, M. Shamsul Emdadul Haque, Md Bellal Hossain, Md |
| description | Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for
[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
b
0
]
)
while the existing solution is determined for a particular case, especially for
[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
0
]
. The solution is easily transformed to perturbation solution. The method is used in various non-linear problems possessing second and more than second derivatives. |
| doi_str_mv | 10.1016/j.ijnonlinmec.2007.05.007 |
| format | article |
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[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
b
0
]
)
while the existing solution is determined for a particular case, especially for
[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
0
]
. The solution is easily transformed to perturbation solution. The method is used in various non-linear problems possessing second and more than second derivatives.</description><identifier>ISSN: 0020-7462</identifier><identifier>EISSN: 1878-5638</identifier><identifier>DOI: 10.1016/j.ijnonlinmec.2007.05.007</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>Asymptotic solution ; Harmonic balance ; Periodic solution</subject><ispartof>International journal of non-linear mechanics, 2007-10, Vol.42 (8), p.1035-1045</ispartof><rights>2007 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c352t-124e6e15b493febd0b506fefc2bc5fd351952b635d1b6598629c429beda523853</citedby><cites>FETCH-LOGICAL-c352t-124e6e15b493febd0b506fefc2bc5fd351952b635d1b6598629c429beda523853</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0020746207001448$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3632,27924,27925,46012</link.rule.ids></links><search><creatorcontrib>Alam, M. Shamsul</creatorcontrib><creatorcontrib>Emdadul Haque, Md</creatorcontrib><creatorcontrib>Bellal Hossain, Md</creatorcontrib><title>A new analytical technique to find periodic solutions of non-linear systems</title><title>International journal of non-linear mechanics</title><description>Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for
[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
b
0
]
)
while the existing solution is determined for a particular case, especially for
[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
0
]
. The solution is easily transformed to perturbation solution. The method is used in various non-linear problems possessing second and more than second derivatives.</description><subject>Asymptotic solution</subject><subject>Harmonic balance</subject><subject>Periodic solution</subject><issn>0020-7462</issn><issn>1878-5638</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNqNkD9PwzAUxC0EEqXwHczClmA7sZOMqOKfqMQCs-XYz8JRahfbBfXb46oMjEy33O_uvUPompKaEipup9pNPvjZ-Q3omhHS1YTXRU7QgvZdX3HR9KdoQQgjVdcKdo4uUppIYVvSLdDLHfbwjZVX8z47rWacQX9497kDnAO2zhu8heiCcRqnMO-yCz7hYHFprUotqIjTPmXYpEt0ZtWc4OpXl-j94f5t9VStXx-fV3frSjec5YqyFgRQPrZDY2E0ZOREWLCajZpb03A6cDaKhhs6Cj70gg26ZcMIRnHW9LxZoptj7jaGcmfKcuOShnlWHsIuyYYMHeXdwTgcjTqGlCJYuY1uo-JeUiIP88lJ_plPHuaThMsihV0dWSiffDmIMmkHXoNxEXSWJrh_pPwA2vB_-w</recordid><startdate>20071001</startdate><enddate>20071001</enddate><creator>Alam, M. Shamsul</creator><creator>Emdadul Haque, Md</creator><creator>Bellal Hossain, Md</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</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></search><sort><creationdate>20071001</creationdate><title>A new analytical technique to find periodic solutions of non-linear systems</title><author>Alam, M. Shamsul ; Emdadul Haque, Md ; Bellal Hossain, Md</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c352t-124e6e15b493febd0b506fefc2bc5fd351952b635d1b6598629c429beda523853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Asymptotic solution</topic><topic>Harmonic balance</topic><topic>Periodic solution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alam, M. Shamsul</creatorcontrib><creatorcontrib>Emdadul Haque, Md</creatorcontrib><creatorcontrib>Bellal Hossain, Md</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems 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>International journal of non-linear mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alam, M. Shamsul</au><au>Emdadul Haque, Md</au><au>Bellal Hossain, Md</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new analytical technique to find periodic solutions of non-linear systems</atitle><jtitle>International journal of non-linear mechanics</jtitle><date>2007-10-01</date><risdate>2007</risdate><volume>42</volume><issue>8</issue><spage>1035</spage><epage>1045</epage><pages>1035-1045</pages><issn>0020-7462</issn><eissn>1878-5638</eissn><abstract>Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for
[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
b
0
]
)
while the existing solution is determined for a particular case, especially for
[
x
(
0
)
=
a
0
,
x
˙
(
0
)
=
0
]
. The solution is easily transformed to perturbation solution. The method is used in various non-linear problems possessing second and more than second derivatives.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.ijnonlinmec.2007.05.007</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0020-7462 |
| ispartof | International journal of non-linear mechanics, 2007-10, Vol.42 (8), p.1035-1045 |
| issn | 0020-7462 1878-5638 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_30971575 |
| source | ScienceDirect Freedom Collection; ScienceDirect: Physics General Backfile |
| subjects | Asymptotic solution Harmonic balance Periodic solution |
| title | A new analytical technique to find periodic solutions of non-linear systems |
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