Symplectic Method for the Thin Piezoelectric Plates
The symplectic method for a thin piezoelectric plate problem is developed. The Hamiltonian canonical equation of thin piezoelectric plate is given by using the variational principle. By applying the separation of variables method, we can obtain symplectic orthogonal eigensolutions. As an application...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/12/5/681 |
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| author | Junjie Fan Lianhe Li Alatancang Chen |
| author_facet | Junjie Fan Lianhe Li Alatancang Chen |
| author_sort | Junjie Fan |
| collection | DOAJ |
| description | The symplectic method for a thin piezoelectric plate problem is developed. The Hamiltonian canonical equation of thin piezoelectric plate is given by using the variational principle. By applying the separation of variables method, we can obtain symplectic orthogonal eigensolutions. As an application, the problem of a thin piezoelectric plate with full edges simply supported under a uniformly distributed load is discussed, and analytical solutions of the deflection and potential of a piezoelectric thin plate are obtained. A numerical example shows that the solutions converge very rapidly. The advantage of this method is that it does not need to assume the predetermined function in advance, so it has better universality. It may also be applied to the problem of thin piezoelectric plate buckling and vibrating. |
| first_indexed | 2024-03-10T03:04:30Z |
| format | Article |
| id | doaj.art-1e032d69b37b47a3a73fd0fa937c78ba |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-10T03:04:30Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-1e032d69b37b47a3a73fd0fa937c78ba2023-11-23T10:35:25ZengMDPI AGCrystals2073-43522022-05-0112568110.3390/cryst12050681Symplectic Method for the Thin Piezoelectric PlatesJunjie Fan0Lianhe Li1Alatancang Chen2College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, ChinaCollege of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, ChinaCollege of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, ChinaThe symplectic method for a thin piezoelectric plate problem is developed. The Hamiltonian canonical equation of thin piezoelectric plate is given by using the variational principle. By applying the separation of variables method, we can obtain symplectic orthogonal eigensolutions. As an application, the problem of a thin piezoelectric plate with full edges simply supported under a uniformly distributed load is discussed, and analytical solutions of the deflection and potential of a piezoelectric thin plate are obtained. A numerical example shows that the solutions converge very rapidly. The advantage of this method is that it does not need to assume the predetermined function in advance, so it has better universality. It may also be applied to the problem of thin piezoelectric plate buckling and vibrating.https://www.mdpi.com/2073-4352/12/5/681symplectic methodHamilton canonical equationsthin piezoelectric plateanalytical solutions |
| spellingShingle | Junjie Fan Lianhe Li Alatancang Chen Symplectic Method for the Thin Piezoelectric Plates Crystals symplectic method Hamilton canonical equations thin piezoelectric plate analytical solutions |
| title | Symplectic Method for the Thin Piezoelectric Plates |
| title_full | Symplectic Method for the Thin Piezoelectric Plates |
| title_fullStr | Symplectic Method for the Thin Piezoelectric Plates |
| title_full_unstemmed | Symplectic Method for the Thin Piezoelectric Plates |
| title_short | Symplectic Method for the Thin Piezoelectric Plates |
| title_sort | symplectic method for the thin piezoelectric plates |
| topic | symplectic method Hamilton canonical equations thin piezoelectric plate analytical solutions |
| url | https://www.mdpi.com/2073-4352/12/5/681 |
| work_keys_str_mv | AT junjiefan symplecticmethodforthethinpiezoelectricplates AT lianheli symplecticmethodforthethinpiezoelectricplates AT alatancangchen symplecticmethodforthethinpiezoelectricplates |