On Non-linear Free Vibrations of a Beam with Pinned Ends
The free vibration of a pinned end beam undergoing large transverse deflection is examined. The equation of motion for this problem is reduced to a Duffing-type equation with a small perturbation parameter. The method of multiple scales is used to determine a uniformly valid higher third order pertu...
| Published in: | Journal of King Saud University: Engineering Sciences |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer
1995-01-01
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018363918306196 |
| _version_ | 1848651154668388352 |
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| author | Mosad A. Foda |
| author_facet | Mosad A. Foda |
| author_sort | Mosad A. Foda |
| collection | DOAJ |
| container_title | Journal of King Saud University: Engineering Sciences |
| description | The free vibration of a pinned end beam undergoing large transverse deflection is examined. The equation of motion for this problem is reduced to a Duffing-type equation with a small perturbation parameter. The method of multiple scales is used to determine a uniformly valid higher third order perturbation solution. The predictions of the non-linear frequencies are in excellent agreement with the exact solution obtained from the direct integration of elliptic integral. Also presented are the harmonic contents of the non-linear transverse displacement. |
| format | Article |
| id | doaj-ecc719f2bbd44651be82f761243cf631 |
| institution | Directory of Open Access Journals |
| issn | 1018-3639 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Springer |
| record_format | Article |
| spelling | doaj-ecc719f2bbd44651be82f761243cf6312025-11-03T01:28:04ZengSpringerJournal of King Saud University: Engineering Sciences1018-36391995-01-01719310610.1016/S1018-3639(18)30619-6On Non-linear Free Vibrations of a Beam with Pinned EndsMosad A. Foda0Mechanical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi ArabiaThe free vibration of a pinned end beam undergoing large transverse deflection is examined. The equation of motion for this problem is reduced to a Duffing-type equation with a small perturbation parameter. The method of multiple scales is used to determine a uniformly valid higher third order perturbation solution. The predictions of the non-linear frequencies are in excellent agreement with the exact solution obtained from the direct integration of elliptic integral. Also presented are the harmonic contents of the non-linear transverse displacement.http://www.sciencedirect.com/science/article/pii/S1018363918306196 |
| spellingShingle | Mosad A. Foda On Non-linear Free Vibrations of a Beam with Pinned Ends |
| title | On Non-linear Free Vibrations of a Beam with Pinned Ends |
| title_full | On Non-linear Free Vibrations of a Beam with Pinned Ends |
| title_fullStr | On Non-linear Free Vibrations of a Beam with Pinned Ends |
| title_full_unstemmed | On Non-linear Free Vibrations of a Beam with Pinned Ends |
| title_short | On Non-linear Free Vibrations of a Beam with Pinned Ends |
| title_sort | on non linear free vibrations of a beam with pinned ends |
| url | http://www.sciencedirect.com/science/article/pii/S1018363918306196 |
| work_keys_str_mv | AT mosadafoda onnonlinearfreevibrationsofabeamwithpinnedends |