Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application
Two criteria are constructed to guarantee the existence of periodic solutions for a second-order -dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system’s damping coefficient, natural frequency, parametric...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/140173 |
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| author | F. B. Gao |
| author_facet | F. B. Gao |
| author_sort | F. B. Gao |
| collection | DOAJ |
| description | Two criteria are constructed to guarantee the existence of periodic solutions for a second-order -dimensional differential system by using continuation theorem. It is noticed that
the criteria established are found to be associated with the system’s damping coefficient, natural
frequency, parametrical excitation, and the coefficient of the nonlinear term.
Based on the criteria obtained, we investigate the periodic motions of the simply supported at
the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent
range of periodic solutions for the thin plate system increases along with the increase of the ratio of
the modulus of nonlinear term’s coefficient and parametric excitation term, which generalize and
improve the corresponding achievements given in the known literature. |
| format | Article |
| id | doaj-art-df4d6ba097b8483e8d307a82324aa108 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-df4d6ba097b8483e8d307a82324aa1082025-02-03T01:13:11ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/140173140173Nontrivial Periodic Solutions of an -Dimensional Differential System and Its ApplicationF. B. Gao0School of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaTwo criteria are constructed to guarantee the existence of periodic solutions for a second-order -dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system’s damping coefficient, natural frequency, parametrical excitation, and the coefficient of the nonlinear term. Based on the criteria obtained, we investigate the periodic motions of the simply supported at the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent range of periodic solutions for the thin plate system increases along with the increase of the ratio of the modulus of nonlinear term’s coefficient and parametric excitation term, which generalize and improve the corresponding achievements given in the known literature.http://dx.doi.org/10.1155/2013/140173 |
| spellingShingle | F. B. Gao Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application Abstract and Applied Analysis |
| title | Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application |
| title_full | Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application |
| title_fullStr | Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application |
| title_full_unstemmed | Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application |
| title_short | Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application |
| title_sort | nontrivial periodic solutions of an dimensional differential system and its application |
| url | http://dx.doi.org/10.1155/2013/140173 |
| work_keys_str_mv | AT fbgao nontrivialperiodicsolutionsofandimensionaldifferentialsystemanditsapplication |