Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method
This paper proposes a new technique based on double parametric form of fuzzy numbers to handle the uncertain vibration equation for very large membrane for different particular cases. Uncertainties present in the initial condition and the wave velocity of free vibration are modelled through Gaussian...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/308205 |
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| author | Smita Tapaswini S. Chakraverty |
| author_facet | Smita Tapaswini S. Chakraverty |
| author_sort | Smita Tapaswini |
| collection | DOAJ |
| description | This paper proposes a new technique based on double parametric form of fuzzy numbers to handle the uncertain vibration equation for very large membrane for different particular cases. Uncertainties present in the initial condition and the wave velocity of free vibration are modelled through Gaussian convex normalised fuzzy set. Using the single parametric form of fuzzy number, the original fuzzy vibration equation is converted first to an interval fuzzy vibration equation. Next this equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same governing equation is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds. The present methods are very simple and effective. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the present analysis. Results obtained by the methods with new techniques are compared with existing results in special cases. |
| format | Article |
| id | doaj-art-9e5025e6c9cb416bbc1373c99777ae50 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-9e5025e6c9cb416bbc1373c99777ae502025-02-03T00:59:56ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/308205308205Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition MethodSmita Tapaswini0S. Chakraverty1Department of Mathematics, National Institute of Technology, Rourkela, Odisha 769 008, IndiaDepartment of Mathematics, National Institute of Technology, Rourkela, Odisha 769 008, IndiaThis paper proposes a new technique based on double parametric form of fuzzy numbers to handle the uncertain vibration equation for very large membrane for different particular cases. Uncertainties present in the initial condition and the wave velocity of free vibration are modelled through Gaussian convex normalised fuzzy set. Using the single parametric form of fuzzy number, the original fuzzy vibration equation is converted first to an interval fuzzy vibration equation. Next this equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same governing equation is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds. The present methods are very simple and effective. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the present analysis. Results obtained by the methods with new techniques are compared with existing results in special cases.http://dx.doi.org/10.1155/2014/308205 |
| spellingShingle | Smita Tapaswini S. Chakraverty Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method The Scientific World Journal |
| title | Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method |
| title_full | Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method |
| title_fullStr | Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method |
| title_full_unstemmed | Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method |
| title_short | Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method |
| title_sort | non probabilistic solution of uncertain vibration equation of large membranes using adomian decomposition method |
| url | http://dx.doi.org/10.1155/2014/308205 |
| work_keys_str_mv | AT smitatapaswini nonprobabilisticsolutionofuncertainvibrationequationoflargemembranesusingadomiandecompositionmethod AT schakraverty nonprobabilisticsolutionofuncertainvibrationequationoflargemembranesusingadomiandecompositionmethod |