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The Scientific World Journal
Volume 2014, Article ID 308205, 11 pages
http://dx.doi.org/10.1155/2014/308205
Research Article

Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method

Department of Mathematics, National Institute of Technology, Rourkela, Odisha 769 008, India

Received 30 August 2013; Accepted 25 December 2013; Published 24 February 2014

Academic Editors: Y. Sawano, Y. C. Shiah, and C. Zhai

Copyright © 2014 Smita Tapaswini and S. Chakraverty. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.