The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method
This paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and H...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2021-09-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/1461348420946574 |
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| _version_ | 1850107154368823296 |
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| author | Xu Liang Zeng Cao Yu Deng Xue Jiang Xing Zha Jianxing Leng |
| author_facet | Xu Liang Zeng Cao Yu Deng Xue Jiang Xing Zha Jianxing Leng |
| author_sort | Xu Liang |
| collection | DOAJ |
| description | This paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and Hamilton’s principle. This paper proposes a novel semi-analytical methodology, which integrates Laplace transform, the one-dimensional differential quadrature method, Fourier series expansion technique, and Laplace numerical inversion to analyze plates’ transient response. The proposed method can obtain dynamic response of the rectangular efficiently and accurately, which fills the gap of transient behaviors in semi-analytical method. A comparison between semi-analytical results and numerical solutions from the publication on this subject is presented to verify the method. Specifically, the results also agree well with the data generated by the Navier’s method. The convergence tests indicate that the semi-analytical algorithm is a quick convergence method. The effects of various variables, such as geometry, boundary conditions, temperature, and the coefficients of the Pasternak foundation, are further studied. The parametric studies show that geometry and temperature change are significant factors that affect the dynamic response of the plate. |
| format | Article |
| id | doaj-art-4444b88910e34af187fe1884b1cb4fd7 |
| institution | OA Journals |
| issn | 1461-3484 2048-4046 |
| language | English |
| publishDate | 2021-09-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj-art-4444b88910e34af187fe1884b1cb4fd72025-08-20T02:38:39ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462021-09-014010.1177/1461348420946574The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical methodXu LiangZeng CaoYu DengXue JiangXing ZhaJianxing LengThis paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and Hamilton’s principle. This paper proposes a novel semi-analytical methodology, which integrates Laplace transform, the one-dimensional differential quadrature method, Fourier series expansion technique, and Laplace numerical inversion to analyze plates’ transient response. The proposed method can obtain dynamic response of the rectangular efficiently and accurately, which fills the gap of transient behaviors in semi-analytical method. A comparison between semi-analytical results and numerical solutions from the publication on this subject is presented to verify the method. Specifically, the results also agree well with the data generated by the Navier’s method. The convergence tests indicate that the semi-analytical algorithm is a quick convergence method. The effects of various variables, such as geometry, boundary conditions, temperature, and the coefficients of the Pasternak foundation, are further studied. The parametric studies show that geometry and temperature change are significant factors that affect the dynamic response of the plate.https://doi.org/10.1177/1461348420946574 |
| spellingShingle | Xu Liang Zeng Cao Yu Deng Xue Jiang Xing Zha Jianxing Leng The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method Journal of Low Frequency Noise, Vibration and Active Control |
| title | The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method |
| title_full | The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method |
| title_fullStr | The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method |
| title_full_unstemmed | The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method |
| title_short | The thermal and Pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi-analytical method |
| title_sort | thermal and pasternak foundation effect on the transient behaviors of the rectangular plate using a novel semi analytical method |
| url | https://doi.org/10.1177/1461348420946574 |
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