Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams
This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constraine...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/280256 |
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| author | Ramazan-Ali Jafari-Talookolaei Maryam Abedi |
| author_facet | Ramazan-Ali Jafari-Talookolaei Maryam Abedi |
| author_sort | Ramazan-Ali Jafari-Talookolaei |
| collection | DOAJ |
| description | This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology. |
| format | Article |
| id | doaj-art-2fc8bf70d966447fb32426bb6357ed15 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-2fc8bf70d966447fb32426bb6357ed152025-02-03T01:31:14ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/280256280256Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko BeamsRamazan-Ali Jafari-Talookolaei0Maryam Abedi1Department of Mechanical Engineering, Islamic Azad University, Sari Branch, Mazandaran Province, Sari 48161-194, IranSchool of Mechanical Engineering, Sharif University of Technology, Tehran 14588-89694, IranThis work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology.http://dx.doi.org/10.1155/2014/280256 |
| spellingShingle | Ramazan-Ali Jafari-Talookolaei Maryam Abedi Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams The Scientific World Journal |
| title | Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams |
| title_full | Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams |
| title_fullStr | Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams |
| title_full_unstemmed | Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams |
| title_short | Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams |
| title_sort | analytical solution for the free vibration analysis of delaminated timoshenko beams |
| url | http://dx.doi.org/10.1155/2014/280256 |
| work_keys_str_mv | AT ramazanalijafaritalookolaei analyticalsolutionforthefreevibrationanalysisofdelaminatedtimoshenkobeams AT maryamabedi analyticalsolutionforthefreevibrationanalysisofdelaminatedtimoshenkobeams |