Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation
The aim of this paper is to reveal the effectiveness of Adomian decomposition method (ADM) and differential transform method (DTM) on free vibrations of axial-loaded Timoshenko beams resting on viscoelastic foundation. The effects of axial compressive load, modulus of subgrade reaction and foundatio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-12-01
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| Series: | Engineering Science and Technology, an International Journal |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215098618307122 |
| _version_ | 1819081142021652480 |
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| author | Baran Bozyigit Yusuf Yesilce Seval Catal |
| author_facet | Baran Bozyigit Yusuf Yesilce Seval Catal |
| author_sort | Baran Bozyigit |
| collection | DOAJ |
| description | The aim of this paper is to reveal the effectiveness of Adomian decomposition method (ADM) and differential transform method (DTM) on free vibrations of axial-loaded Timoshenko beams resting on viscoelastic foundation. The effects of axial compressive load, modulus of subgrade reaction and foundation damping on natural frequencies of beam model are studied using various boundary conditions. The results of DTM and ADM are tabulated with exact results that obtained from analytical formulations where an excellent agreement is observed. Moreover, the dynamic stiffness method (DSM) which uses the exact mode shapes is applied to verify the analytical results. The accuracy of mathematical tools DTM and ADM is demonstrated by several numerical examples. The first four mode shapes are depicted. It is highlighted that application of DTM, ADM and DSM can be extended without any difficulties for free vibrations of beam assembly structures that resting on viscoelastic foundation. Keywords: Adomian decomposition method, Axial-loaded Timoshenko beam, Differential transformation, Dynamic stiffness method, Free vibration, Foundation damping |
| first_indexed | 2024-12-21T19:56:04Z |
| format | Article |
| id | doaj.art-b4be990cc65b4b50b9efcdd8ad8fc5c5 |
| institution | Directory Open Access Journal |
| issn | 2215-0986 |
| language | English |
| last_indexed | 2024-12-21T19:56:04Z |
| publishDate | 2018-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Engineering Science and Technology, an International Journal |
| spelling | doaj.art-b4be990cc65b4b50b9efcdd8ad8fc5c52022-12-21T18:52:05ZengElsevierEngineering Science and Technology, an International Journal2215-09862018-12-0121611811193Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformationBaran Bozyigit0Yusuf Yesilce1Seval Catal2Corresponding author.; Dokuz Eylul University, Department of Civil Engineering, 35160, Buca, Izmir, TurkeyDokuz Eylul University, Department of Civil Engineering, 35160, Buca, Izmir, TurkeyDokuz Eylul University, Department of Civil Engineering, 35160, Buca, Izmir, TurkeyThe aim of this paper is to reveal the effectiveness of Adomian decomposition method (ADM) and differential transform method (DTM) on free vibrations of axial-loaded Timoshenko beams resting on viscoelastic foundation. The effects of axial compressive load, modulus of subgrade reaction and foundation damping on natural frequencies of beam model are studied using various boundary conditions. The results of DTM and ADM are tabulated with exact results that obtained from analytical formulations where an excellent agreement is observed. Moreover, the dynamic stiffness method (DSM) which uses the exact mode shapes is applied to verify the analytical results. The accuracy of mathematical tools DTM and ADM is demonstrated by several numerical examples. The first four mode shapes are depicted. It is highlighted that application of DTM, ADM and DSM can be extended without any difficulties for free vibrations of beam assembly structures that resting on viscoelastic foundation. Keywords: Adomian decomposition method, Axial-loaded Timoshenko beam, Differential transformation, Dynamic stiffness method, Free vibration, Foundation dampinghttp://www.sciencedirect.com/science/article/pii/S2215098618307122 |
| spellingShingle | Baran Bozyigit Yusuf Yesilce Seval Catal Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation Engineering Science and Technology, an International Journal |
| title | Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation |
| title_full | Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation |
| title_fullStr | Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation |
| title_full_unstemmed | Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation |
| title_short | Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation |
| title_sort | free vibrations of axial loaded beams resting on viscoelastic foundation using adomian decomposition method and differential transformation |
| url | http://www.sciencedirect.com/science/article/pii/S2215098618307122 |
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