Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions
Abstract This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any exist...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-02-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-29044-7 |
| _version_ | 1797864911573876736 |
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| author | Zhaoyang Hu Jingyu Du Mingfeng Liu Yihao Li Zixuan Wang Xinran Zheng Tinh Quoc Bui Rui Li |
| author_facet | Zhaoyang Hu Jingyu Du Mingfeng Liu Yihao Li Zixuan Wang Xinran Zheng Tinh Quoc Bui Rui Li |
| author_sort | Zhaoyang Hu |
| collection | DOAJ |
| description | Abstract This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any existing works. Such analytic solutions are not accessible through conventional analytic methods as seeking analytic solutions that meet both the governing partial differential equations and various non-Lévy-type boundary conditions is an acknowledged challenge in mechanical analysis of plates. The clamped and free plates are considered as two most representative cases of non-Lévy-type plates. The SSM is implemented in the Hamiltonian system-based symplectic space, where the separation of variables and the symplectic eigen expansion prove to be well-grounded. These two mathematical treatments are adopted to first gain the analytic solutions of two elementary problems. The final analytic free in-plane vibration solutions are obtained by superposition of the two elementary problems. Comprehensive new natural frequencies and vibration modes are studied and validated by reference solutions from the finite element method or other approaches. The rigorous solution procedure, fast convergence, and highly accurate results render the present framework capable of serving as benchmarks for future comparison and applicable to analytic investigation of more plate problems. |
| first_indexed | 2024-04-09T23:00:48Z |
| format | Article |
| id | doaj.art-74ec3211184a4f16910c8bcf3b9fcb1c |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-09T23:00:48Z |
| publishDate | 2023-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-74ec3211184a4f16910c8bcf3b9fcb1c2023-03-22T11:01:43ZengNature PortfolioScientific Reports2045-23222023-02-0113111310.1038/s41598-023-29044-7Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditionsZhaoyang Hu0Jingyu Du1Mingfeng Liu2Yihao Li3Zixuan Wang4Xinran Zheng5Tinh Quoc Bui6Rui Li7State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of TechnologyState Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of TechnologyState Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of TechnologyState Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of TechnologyState Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of TechnologyState Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of TechnologyDuy Tan Research Institute for Computational Engineering (DTRICE), Duy Tan UniversityState Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of TechnologyAbstract This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any existing works. Such analytic solutions are not accessible through conventional analytic methods as seeking analytic solutions that meet both the governing partial differential equations and various non-Lévy-type boundary conditions is an acknowledged challenge in mechanical analysis of plates. The clamped and free plates are considered as two most representative cases of non-Lévy-type plates. The SSM is implemented in the Hamiltonian system-based symplectic space, where the separation of variables and the symplectic eigen expansion prove to be well-grounded. These two mathematical treatments are adopted to first gain the analytic solutions of two elementary problems. The final analytic free in-plane vibration solutions are obtained by superposition of the two elementary problems. Comprehensive new natural frequencies and vibration modes are studied and validated by reference solutions from the finite element method or other approaches. The rigorous solution procedure, fast convergence, and highly accurate results render the present framework capable of serving as benchmarks for future comparison and applicable to analytic investigation of more plate problems.https://doi.org/10.1038/s41598-023-29044-7 |
| spellingShingle | Zhaoyang Hu Jingyu Du Mingfeng Liu Yihao Li Zixuan Wang Xinran Zheng Tinh Quoc Bui Rui Li Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions Scientific Reports |
| title | Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions |
| title_full | Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions |
| title_fullStr | Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions |
| title_full_unstemmed | Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions |
| title_short | Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions |
| title_sort | symplectic superposition solutions for free in plane vibration of orthotropic rectangular plates with general boundary conditions |
| url | https://doi.org/10.1038/s41598-023-29044-7 |
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