New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method
The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solution...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhaoying Wu [verfasserIn] An Li [verfasserIn] Yu Wu [verfasserIn] Zhiming Yin [verfasserIn] Salamat Ullah [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
In: Buildings - MDPI AG, 2012, 14(2024), 3, p 687 |
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| Übergeordnetes Werk: |
volume:14 ; year:2024 ; number:3, p 687 |
| Links: |
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| DOI / URN: |
10.3390/buildings14030687 |
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DOAJ100539807 |
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| 520 | |a The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. | ||
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10.3390/buildings14030687 doi (DE-627)DOAJ100539807 (DE-599)DOAJ46b485df74ff4bcf92cab928a40272a4 DE-627 ger DE-627 rakwb eng TH1-9745 Zhaoying Wu verfasserin aut New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. free vibration behaviors orthotropic rectangular thin plates two-dimensional modified Fourier series method Building construction An Li verfasserin aut Yu Wu verfasserin aut Zhiming Yin verfasserin aut Salamat Ullah verfasserin aut In Buildings MDPI AG, 2012 14(2024), 3, p 687 (DE-627)718622251 (DE-600)2661539-3 20755309 nnns volume:14 year:2024 number:3, p 687 https://doi.org/10.3390/buildings14030687 kostenfrei https://doaj.org/article/46b485df74ff4bcf92cab928a40272a4 kostenfrei https://www.mdpi.com/2075-5309/14/3/687 kostenfrei https://doaj.org/toc/2075-5309 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 14 2024 3, p 687 |
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10.3390/buildings14030687 doi (DE-627)DOAJ100539807 (DE-599)DOAJ46b485df74ff4bcf92cab928a40272a4 DE-627 ger DE-627 rakwb eng TH1-9745 Zhaoying Wu verfasserin aut New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. free vibration behaviors orthotropic rectangular thin plates two-dimensional modified Fourier series method Building construction An Li verfasserin aut Yu Wu verfasserin aut Zhiming Yin verfasserin aut Salamat Ullah verfasserin aut In Buildings MDPI AG, 2012 14(2024), 3, p 687 (DE-627)718622251 (DE-600)2661539-3 20755309 nnns volume:14 year:2024 number:3, p 687 https://doi.org/10.3390/buildings14030687 kostenfrei https://doaj.org/article/46b485df74ff4bcf92cab928a40272a4 kostenfrei https://www.mdpi.com/2075-5309/14/3/687 kostenfrei https://doaj.org/toc/2075-5309 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 14 2024 3, p 687 |
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10.3390/buildings14030687 doi (DE-627)DOAJ100539807 (DE-599)DOAJ46b485df74ff4bcf92cab928a40272a4 DE-627 ger DE-627 rakwb eng TH1-9745 Zhaoying Wu verfasserin aut New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. free vibration behaviors orthotropic rectangular thin plates two-dimensional modified Fourier series method Building construction An Li verfasserin aut Yu Wu verfasserin aut Zhiming Yin verfasserin aut Salamat Ullah verfasserin aut In Buildings MDPI AG, 2012 14(2024), 3, p 687 (DE-627)718622251 (DE-600)2661539-3 20755309 nnns volume:14 year:2024 number:3, p 687 https://doi.org/10.3390/buildings14030687 kostenfrei https://doaj.org/article/46b485df74ff4bcf92cab928a40272a4 kostenfrei https://www.mdpi.com/2075-5309/14/3/687 kostenfrei https://doaj.org/toc/2075-5309 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 14 2024 3, p 687 |
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10.3390/buildings14030687 doi (DE-627)DOAJ100539807 (DE-599)DOAJ46b485df74ff4bcf92cab928a40272a4 DE-627 ger DE-627 rakwb eng TH1-9745 Zhaoying Wu verfasserin aut New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. free vibration behaviors orthotropic rectangular thin plates two-dimensional modified Fourier series method Building construction An Li verfasserin aut Yu Wu verfasserin aut Zhiming Yin verfasserin aut Salamat Ullah verfasserin aut In Buildings MDPI AG, 2012 14(2024), 3, p 687 (DE-627)718622251 (DE-600)2661539-3 20755309 nnns volume:14 year:2024 number:3, p 687 https://doi.org/10.3390/buildings14030687 kostenfrei https://doaj.org/article/46b485df74ff4bcf92cab928a40272a4 kostenfrei https://www.mdpi.com/2075-5309/14/3/687 kostenfrei https://doaj.org/toc/2075-5309 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 14 2024 3, p 687 |
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10.3390/buildings14030687 doi (DE-627)DOAJ100539807 (DE-599)DOAJ46b485df74ff4bcf92cab928a40272a4 DE-627 ger DE-627 rakwb eng TH1-9745 Zhaoying Wu verfasserin aut New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. free vibration behaviors orthotropic rectangular thin plates two-dimensional modified Fourier series method Building construction An Li verfasserin aut Yu Wu verfasserin aut Zhiming Yin verfasserin aut Salamat Ullah verfasserin aut In Buildings MDPI AG, 2012 14(2024), 3, p 687 (DE-627)718622251 (DE-600)2661539-3 20755309 nnns volume:14 year:2024 number:3, p 687 https://doi.org/10.3390/buildings14030687 kostenfrei https://doaj.org/article/46b485df74ff4bcf92cab928a40272a4 kostenfrei https://www.mdpi.com/2075-5309/14/3/687 kostenfrei https://doaj.org/toc/2075-5309 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 14 2024 3, p 687 |
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New Natural Frequency Studies of Orthotropic Plates by Adopting a Two-Dimensional Modified Fourier Series Method |
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The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. |
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The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. |
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The free vibration behavior of orthotropic thin plates, which are clamped at three edges and free at one edge, is a matter of great concern in the engineering field. Various numerical/approximate approaches have been proposed for the present problem; however, lack precise analytic benchmark solutions are lacking in the literature. In the present study, we propose a modified two-dimensional Fourier series method to effectively handle free vibration problems of plates under various edge conditions. In the given solution, the adopted trial function automatically satisfies several boundary conditions. After imposing Stoke’s transformation in the trial function and letting it satisfy the remaining boundary conditions, we can change the present plate problem into calculating several systems of linear algebra equations which are easily handled. The present method can be regarded as an easily implemented, rational, and rigorous approach, as it can exactly satisfy both the governing equation and the associated edge conditions. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through the utilization of different types of Fourier series, and it can be extended for the further dynamic/static analysis of plates under different shear deformation theories. Finally, all the novel analytical solutions are confirmed to be sufficiently accurate since they match well with the FEM results. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods. |
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