Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System
This paper investigates the bifurcation behavior and the stability of the rotating cantilever rectangular plate that is subjected to varying speed and centrifugal force. The local stability of the degenerated equilibrium of nonlinear system with symmetry is observed after analyzing the corresponding...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-03-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/3/629 |
| _version_ | 1797441480473706496 |
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| author | Shuping Chen Danjin Zhang Youhua Qian |
| author_facet | Shuping Chen Danjin Zhang Youhua Qian |
| author_sort | Shuping Chen |
| collection | DOAJ |
| description | This paper investigates the bifurcation behavior and the stability of the rotating cantilever rectangular plate that is subjected to varying speed and centrifugal force. The local stability of the degenerated equilibrium of nonlinear system with symmetry is observed after analyzing the corresponding characteristic equation. In addition to complex phenomena such as static bifurcation and Hopf bifurcation, the 2-D torus bifurcation is investigated in this paper. Thereafter, the steady-state solutions and stability region are obtained using the center manifold theory and normal form method. Finally, numerical simulations are conducted to show the nonlinear dynamical behaviors of the rotating cantilever rectangular plate. |
| first_indexed | 2024-03-09T12:23:41Z |
| format | Article |
| id | doaj.art-60e7a7edbc0a4ad2befdcfad79c72447 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T12:23:41Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-60e7a7edbc0a4ad2befdcfad79c724472023-11-30T22:37:16ZengMDPI AGSymmetry2073-89942022-03-0114362910.3390/sym14030629Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate SystemShuping Chen0Danjin Zhang1Youhua Qian2College of Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaThis paper investigates the bifurcation behavior and the stability of the rotating cantilever rectangular plate that is subjected to varying speed and centrifugal force. The local stability of the degenerated equilibrium of nonlinear system with symmetry is observed after analyzing the corresponding characteristic equation. In addition to complex phenomena such as static bifurcation and Hopf bifurcation, the 2-D torus bifurcation is investigated in this paper. Thereafter, the steady-state solutions and stability region are obtained using the center manifold theory and normal form method. Finally, numerical simulations are conducted to show the nonlinear dynamical behaviors of the rotating cantilever rectangular plate.https://www.mdpi.com/2073-8994/14/3/629bifurcationstabilityrotating cantilever plate |
| spellingShingle | Shuping Chen Danjin Zhang Youhua Qian Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System Symmetry bifurcation stability rotating cantilever plate |
| title | Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System |
| title_full | Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System |
| title_fullStr | Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System |
| title_full_unstemmed | Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System |
| title_short | Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System |
| title_sort | stability and bifurcation analysis of a nonlinear rotating cantilever plate system |
| topic | bifurcation stability rotating cantilever plate |
| url | https://www.mdpi.com/2073-8994/14/3/629 |
| work_keys_str_mv | AT shupingchen stabilityandbifurcationanalysisofanonlinearrotatingcantileverplatesystem AT danjinzhang stabilityandbifurcationanalysisofanonlinearrotatingcantileverplatesystem AT youhuaqian stabilityandbifurcationanalysisofanonlinearrotatingcantileverplatesystem |