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Applied Computational Intelligence and Soft Computing
Volume 2013 (2013), Article ID 764871, 8 pages
http://dx.doi.org/10.1155/2013/764871
Research Article

Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers

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

Received 31 March 2013; Revised 17 June 2013; Accepted 11 September 2013

Academic Editor: Christian W. Dawson

Copyright © 2013 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

Present paper proposes a new technique to solve uncertain beam equation using double parametric form of fuzzy numbers. Uncertainties appearing in the initial conditions are taken in terms of triangular fuzzy number. Using the single parametric form, the fuzzy beam equation is converted first to an interval-based fuzzy differential equation. Next, this differential equation is transformed to crisp form by applying double parametric form of fuzzy number. Finally, the same is solved by homotopy perturbation method (HPM) to obtain the uncertain responses subject to unit step and impulse loads. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the methodology.