Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions
In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wang, Zekun [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020transfer abstract |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Cancer of the uterus and treatment of incontinence (CUTI) - Robison, K.M. ELSEVIER, 2015, London |
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| Übergeordnetes Werk: |
volume:470 ; year:2020 ; day:31 ; month:03 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.jsv.2019.115166 |
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ELV04914684X |
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| 520 | |a In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. | ||
| 520 | |a In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. | ||
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10.1016/j.jsv.2019.115166 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000885.pica (DE-627)ELV04914684X (ELSEVIER)S0022-460X(19)30729-1 DE-627 ger DE-627 rakwb eng 610 VZ 610 VZ 44.11 bkl Wang, Zekun verfasserin aut Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. Rectangular plates Elsevier Arbitrary homogeneous boundary conditions Elsevier Closed-form solutions Elsevier Free in-plane vibration Elsevier Xing, Yufeng oth Sun, Qiaozhen oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:470 year:2020 day:31 month:03 pages:0 https://doi.org/10.1016/j.jsv.2019.115166 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 470 2020 31 0331 0 |
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10.1016/j.jsv.2019.115166 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000885.pica (DE-627)ELV04914684X (ELSEVIER)S0022-460X(19)30729-1 DE-627 ger DE-627 rakwb eng 610 VZ 610 VZ 44.11 bkl Wang, Zekun verfasserin aut Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. Rectangular plates Elsevier Arbitrary homogeneous boundary conditions Elsevier Closed-form solutions Elsevier Free in-plane vibration Elsevier Xing, Yufeng oth Sun, Qiaozhen oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:470 year:2020 day:31 month:03 pages:0 https://doi.org/10.1016/j.jsv.2019.115166 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 470 2020 31 0331 0 |
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10.1016/j.jsv.2019.115166 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000885.pica (DE-627)ELV04914684X (ELSEVIER)S0022-460X(19)30729-1 DE-627 ger DE-627 rakwb eng 610 VZ 610 VZ 44.11 bkl Wang, Zekun verfasserin aut Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. Rectangular plates Elsevier Arbitrary homogeneous boundary conditions Elsevier Closed-form solutions Elsevier Free in-plane vibration Elsevier Xing, Yufeng oth Sun, Qiaozhen oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:470 year:2020 day:31 month:03 pages:0 https://doi.org/10.1016/j.jsv.2019.115166 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 470 2020 31 0331 0 |
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10.1016/j.jsv.2019.115166 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000885.pica (DE-627)ELV04914684X (ELSEVIER)S0022-460X(19)30729-1 DE-627 ger DE-627 rakwb eng 610 VZ 610 VZ 44.11 bkl Wang, Zekun verfasserin aut Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. Rectangular plates Elsevier Arbitrary homogeneous boundary conditions Elsevier Closed-form solutions Elsevier Free in-plane vibration Elsevier Xing, Yufeng oth Sun, Qiaozhen oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:470 year:2020 day:31 month:03 pages:0 https://doi.org/10.1016/j.jsv.2019.115166 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 470 2020 31 0331 0 |
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10.1016/j.jsv.2019.115166 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000000885.pica (DE-627)ELV04914684X (ELSEVIER)S0022-460X(19)30729-1 DE-627 ger DE-627 rakwb eng 610 VZ 610 VZ 44.11 bkl Wang, Zekun verfasserin aut Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions 2020transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. Rectangular plates Elsevier Arbitrary homogeneous boundary conditions Elsevier Closed-form solutions Elsevier Free in-plane vibration Elsevier Xing, Yufeng oth Sun, Qiaozhen oth Enthalten in Academic Press Robison, K.M. ELSEVIER Cancer of the uterus and treatment of incontinence (CUTI) 2015 London (DE-627)ELV012704822 volume:470 year:2020 day:31 month:03 pages:0 https://doi.org/10.1016/j.jsv.2019.115166 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_30 GBV_ILN_40 44.11 Präventivmedizin VZ AR 470 2020 31 0331 0 |
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Cancer of the uterus and treatment of incontinence (CUTI) |
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Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions |
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Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions |
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Wang, Zekun |
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Cancer of the uterus and treatment of incontinence (CUTI) |
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Cancer of the uterus and treatment of incontinence (CUTI) |
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10.1016/j.jsv.2019.115166 |
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610 |
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highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions |
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Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions |
| abstract |
In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. |
| abstractGer |
In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. |
| abstract_unstemmed |
In this paper, highly accurate closed-form solutions for the free in-plane vibration of rectangular isotropic plates with arbitrary homogeneous boundary conditions are achieved by an iterative separation-of-variable method, and all solutions are presented in an elegant explicit form. For plates with at least a pair of opposite edges simply supported, the present solutions are the exact solutions. For other homogeneous boundary conditions, the accurate closed-form solutions agree well with the results of the fine finite element method. This work shows that the iterative separation-of-variables method is a powerful method to find the closed-form eigensolutions of partial differential equations. The present solutions can be taken as the benchmarks for the validation of numerical methods, a guide in parametric design of structure and the basis of constructing new numerical methods. |
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Highly accurate closed-form solutions for the free in-plane vibration of rectangular plates with arbitrary homogeneous boundary conditions |
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