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Structural Engineering and Mechanics Volume 37, Number 4, February25 2011 , pages 415-425 DOI: https://doi.org/10.12989/sem.2011.37.4.415 |
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The Homotopy Perturbation Method for free vibration analysis of beam on elastic foundation |
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Baki Ozturk and Safa Bozkurt Coskun
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| Abstract | ||
| In this study, the homotopy perturbation method (HPM) is applied to free vibration analysis of beam on elastic foundation. This numerical method is applied on three different axially loaded cases, namely: 1) one end fixed, the other end simply supported; 2) both ends fixed and 3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, Nr. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for all the cases considered in this study and the differential transform method (DTM) results available in the literature for the fixed-pinned case. | ||
| Key Words | ||
| homotopy perturbation method; beam on elastic foundation; free vibration analysis. | ||
| Address | ||
| Baki Ozturk: Department of Civil Engineering, Faculty of Engineering and Architecture, Nigde University, 51100 Nigde, Turkey Safa Bozkurt Coskun: Department of Civil Engineering, Faculty of Engineering, Kocaeli University, 41380 Kocaeli, Turkey | ||