Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method
Analytical solutions describing free transverse vibrations with large amplitude of axially loaded Euler–Bernoulli beams for various end restrains resting on a Winkler one-parameter foundation are obtained using the Adomian modified decomposition method (AMDM). The AMDM allows the governing equation...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2019/3405075 |
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| author | Desmond Adair Askar Ibrayev Alima Tazabekova Jong R. Kim |
| author_facet | Desmond Adair Askar Ibrayev Alima Tazabekova Jong R. Kim |
| author_sort | Desmond Adair |
| collection | DOAJ |
| description | Analytical solutions describing free transverse vibrations with large amplitude of axially loaded Euler–Bernoulli beams for various end restrains resting on a Winkler one-parameter foundation are obtained using the Adomian modified decomposition method (AMDM). The AMDM allows the governing equation to become a recursive algebraic equation, and, after some additional simple mathematical operations, the equations can be cast as an eigenvector problem whose solution results in the calculation of natural frequencies and corresponding closed-form series solution of the mode shapes. Important to the use of the Adomian modified decomposition method is the treatment of the nonlinear Fredholm integral coefficient, which forms part of the governing equation. In addition to the calculation of natural frequencies and mode shapes, investigations are made of the effects on the free vibrations of the Winkler parameter and of increasing the axial loading. |
| format | Article |
| id | doaj-art-a08bce2c98254efa89f53c8a9ce6833b |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-a08bce2c98254efa89f53c8a9ce6833b2025-02-03T06:15:11ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/34050753405075Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition MethodDesmond Adair0Askar Ibrayev1Alima Tazabekova2Jong R. Kim3Department of Mechanical & Aerospace Engineering, Nazarbayev University, Astana 010000, KazakhstanDepartment of Civil & Environment Engineering, Nazarbayev University, Astana 010000, KazakhstanDepartment of Mechanical & Aerospace Engineering, Nazarbayev University, Astana 010000, KazakhstanDepartment of Civil & Environment Engineering, Nazarbayev University, Astana 010000, KazakhstanAnalytical solutions describing free transverse vibrations with large amplitude of axially loaded Euler–Bernoulli beams for various end restrains resting on a Winkler one-parameter foundation are obtained using the Adomian modified decomposition method (AMDM). The AMDM allows the governing equation to become a recursive algebraic equation, and, after some additional simple mathematical operations, the equations can be cast as an eigenvector problem whose solution results in the calculation of natural frequencies and corresponding closed-form series solution of the mode shapes. Important to the use of the Adomian modified decomposition method is the treatment of the nonlinear Fredholm integral coefficient, which forms part of the governing equation. In addition to the calculation of natural frequencies and mode shapes, investigations are made of the effects on the free vibrations of the Winkler parameter and of increasing the axial loading.http://dx.doi.org/10.1155/2019/3405075 |
| spellingShingle | Desmond Adair Askar Ibrayev Alima Tazabekova Jong R. Kim Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method Shock and Vibration |
| title | Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method |
| title_full | Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method |
| title_fullStr | Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method |
| title_full_unstemmed | Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method |
| title_short | Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method |
| title_sort | free vibrations with large amplitude of axially loaded beams on an elastic foundation using the adomian modified decomposition method |
| url | http://dx.doi.org/10.1155/2019/3405075 |
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