Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance
Stability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1 : 1 internal reson...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/414903 |
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| author | Dongmei Zhang Fangqi Chen |
| author_facet | Dongmei Zhang Fangqi Chen |
| author_sort | Dongmei Zhang |
| collection | DOAJ |
| description | Stability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1 : 1 internal resonances and primary parametric resonance. Two types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, and a double zero and a pair of pure imaginary eigenvalues. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters which may lead to Hopf bifurcation and 2D torus. With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively. A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic predictions. |
| format | Article |
| id | doaj-art-56b443c0598346559b57765891323279 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-56b443c0598346559b577658913232792025-02-03T06:42:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/414903414903Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal ResonanceDongmei Zhang0Fangqi Chen1Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaStability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1 : 1 internal resonances and primary parametric resonance. Two types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, and a double zero and a pair of pure imaginary eigenvalues. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters which may lead to Hopf bifurcation and 2D torus. With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively. A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic predictions.http://dx.doi.org/10.1155/2014/414903 |
| spellingShingle | Dongmei Zhang Fangqi Chen Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance Journal of Applied Mathematics |
| title | Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance |
| title_full | Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance |
| title_fullStr | Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance |
| title_full_unstemmed | Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance |
| title_short | Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance |
| title_sort | stability and bifurcation for a simply supported functionally graded material plate with one to one internal resonance |
| url | http://dx.doi.org/10.1155/2014/414903 |
| work_keys_str_mv | AT dongmeizhang stabilityandbifurcationforasimplysupportedfunctionallygradedmaterialplatewithonetooneinternalresonance AT fangqichen stabilityandbifurcationforasimplysupportedfunctionallygradedmaterialplatewithonetooneinternalresonance |