Exact solution for free in-plane vibration analysis of an eccentric elliptical plate
Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by...
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| Autor*in: |
Hasheminejad, Seyyed M. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Wien 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mechanica - Springer Vienna, 1965, 224(2013), 8 vom: 03. März, Seite 1609-1624 |
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| Übergeordnetes Werk: |
volume:224 ; year:2013 ; number:8 ; day:03 ; month:03 ; pages:1609-1624 |
| Links: |
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| DOI / URN: |
10.1007/s00707-013-0829-y |
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OLC2030138878 |
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| 520 | |a Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. | ||
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10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
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10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
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10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
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10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
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10.1007/s00707-013-0829-y doi (DE-627)OLC2030138878 (DE-He213)s00707-013-0829-y-p DE-627 ger DE-627 rakwb eng 530 VZ Hasheminejad, Seyyed M. verfasserin aut Exact solution for free in-plane vibration analysis of an eccentric elliptical plate 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Wien 2013 Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. Circular Plate Edge Condition Annular Plate Thin Elastic Plate Annular Disk Ghaheri, Ali aut Vaezian, Sajjad aut Enthalten in Acta mechanica Springer Vienna, 1965 224(2013), 8 vom: 03. März, Seite 1609-1624 (DE-627)129511676 (DE-600)210328-X (DE-576)014919141 0001-5970 nnns volume:224 year:2013 number:8 day:03 month:03 pages:1609-1624 https://doi.org/10.1007/s00707-013-0829-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_22 GBV_ILN_59 GBV_ILN_70 GBV_ILN_2020 GBV_ILN_4700 AR 224 2013 8 03 03 1609-1624 |
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Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
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Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. © Springer-Verlag Wien 2013 |
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Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. © Springer-Verlag Wien 2013 |
| abstract_unstemmed |
Abstract A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters. © Springer-Verlag Wien 2013 |
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| title_short |
Exact solution for free in-plane vibration analysis of an eccentric elliptical plate |
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https://doi.org/10.1007/s00707-013-0829-y |
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Ghaheri, Ali Vaezian, Sajjad |
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