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...
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| Format: | Article |
| Language: | English |
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Elsevier
1995-01-01
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| Series: | Journal of King Saud University: Engineering Sciences |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018363918306196 |
| Summary: | 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. |
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| ISSN: | 1018-3639 |