A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation
The aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a p...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/614874 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849396650567532544 |
|---|---|
| author | S. M. Abo-Dahab Mohamed S. Mohamed T. A. Nofal |
| author_facet | S. M. Abo-Dahab Mohamed S. Mohamed T. A. Nofal |
| author_sort | S. M. Abo-Dahab |
| collection | DOAJ |
| description | The aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. This optimal approach has a general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The displacement and temperature are calculated for the models with the variations of the magnetic field, relaxation times, and rotation. The results obtained are displayed graphically to show the influences of the new parameters. |
| format | Article |
| id | doaj-art-b003f656bdc5483587f2996fd7827c0b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b003f656bdc5483587f2996fd7827c0b2025-08-20T03:39:17ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/614874614874A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of RotationS. M. Abo-Dahab0Mohamed S. Mohamed1T. A. Nofal2Mathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi ArabiaMathematics Department, Faculty of Science, Taif University, P.O. Box 888, Saudi ArabiaThe aim of this paper is to apply OHAM to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation, thermal relaxation times, and magnetic field. The problem is solved in one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. This optimal approach has a general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The displacement and temperature are calculated for the models with the variations of the magnetic field, relaxation times, and rotation. The results obtained are displayed graphically to show the influences of the new parameters.http://dx.doi.org/10.1155/2013/614874 |
| spellingShingle | S. M. Abo-Dahab Mohamed S. Mohamed T. A. Nofal A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation Abstract and Applied Analysis |
| title | A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation |
| title_full | A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation |
| title_fullStr | A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation |
| title_full_unstemmed | A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation |
| title_short | A One Step Optimal Homotopy Analysis Method for Propagation of Harmonic Waves in Nonlinear Generalized Magnetothermoelasticity with Two Relaxation Times under Influence of Rotation |
| title_sort | one step optimal homotopy analysis method for propagation of harmonic waves in nonlinear generalized magnetothermoelasticity with two relaxation times under influence of rotation |
| url | http://dx.doi.org/10.1155/2013/614874 |
| work_keys_str_mv | AT smabodahab aonestepoptimalhomotopyanalysismethodforpropagationofharmonicwavesinnonlineargeneralizedmagnetothermoelasticitywithtworelaxationtimesunderinfluenceofrotation AT mohamedsmohamed aonestepoptimalhomotopyanalysismethodforpropagationofharmonicwavesinnonlineargeneralizedmagnetothermoelasticitywithtworelaxationtimesunderinfluenceofrotation AT tanofal aonestepoptimalhomotopyanalysismethodforpropagationofharmonicwavesinnonlineargeneralizedmagnetothermoelasticitywithtworelaxationtimesunderinfluenceofrotation AT smabodahab onestepoptimalhomotopyanalysismethodforpropagationofharmonicwavesinnonlineargeneralizedmagnetothermoelasticitywithtworelaxationtimesunderinfluenceofrotation AT mohamedsmohamed onestepoptimalhomotopyanalysismethodforpropagationofharmonicwavesinnonlineargeneralizedmagnetothermoelasticitywithtworelaxationtimesunderinfluenceofrotation AT tanofal onestepoptimalhomotopyanalysismethodforpropagationofharmonicwavesinnonlineargeneralizedmagnetothermoelasticitywithtworelaxationtimesunderinfluenceofrotation |