An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories
The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse d...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/842805 |
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| author | R. A. Jafari-Talookolaei M. H. Kargarnovin M. T. Ahmadian M. Abedi |
| author_facet | R. A. Jafari-Talookolaei M. H. Kargarnovin M. T. Ahmadian M. Abedi |
| author_sort | R. A. Jafari-Talookolaei |
| collection | DOAJ |
| description | The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed. |
| format | Article |
| id | doaj-art-acffc76ea6584235a85d191c71bfac60 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-acffc76ea6584235a85d191c71bfac602025-02-03T05:58:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/842805842805An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering TheoriesR. A. Jafari-Talookolaei0M. H. Kargarnovin1M. T. Ahmadian2M. Abedi3Young Research Club, Islamic Azad University, Sari Branch, P.O. Box 48161-194, Mazandaran Province, Sari, IranSchool of Mechanical Engineering, Sharif University of Technology, P.O. Box 14588-89694, Tehran, IranSchool of Mechanical Engineering, Sharif University of Technology, P.O. Box 14588-89694, Tehran, IranSchool of Mechanical Engineering, Sharif University of Technology, P.O. Box 14588-89694, Tehran, IranThe objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed.http://dx.doi.org/10.1155/2011/842805 |
| spellingShingle | R. A. Jafari-Talookolaei M. H. Kargarnovin M. T. Ahmadian M. Abedi An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories Journal of Applied Mathematics |
| title | An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories |
| title_full | An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories |
| title_fullStr | An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories |
| title_full_unstemmed | An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories |
| title_short | An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories |
| title_sort | investigation on the nonlinear free vibration analysis of beams with simply supported boundary conditions using four engineering theories |
| url | http://dx.doi.org/10.1155/2011/842805 |
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