# Uncertain vibration equation of large membranes

• Smita Tapaswini
• S. Chakraverty
• Diptiranjan Behera
Regular Article

## Abstract.

The study of the vibration of large membranes is important due to its well-known applications. There exist various investigations for the above problem where the variables and parameters are given as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors propose here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain problem of large membranes. Finally, the problem has been solved using the Homotopy Perturbation Method (HPM). The present method performs very well in terms of computational efficiency. The reliability of the method is shown for obtaining an approximate numerical solution for different cases. Results are given in terms of plots and are also compared in special cases.

### Keywords

Fuzzy Number Parametric Form Triangular Fuzzy Number Homotopy Perturbation Method Vibration Equation

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© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2014

## Authors and Affiliations

• Smita Tapaswini
• 1
• S. Chakraverty
• 1
• Diptiranjan Behera
• 1
1. 1.Department of MathematicsNational Institute of Technology RourkelaOdishaIndia