Direct and Fuzzy Transform Methods for the Stabilization Vibrations of a Damped Linear String

Volume 15, Issue 3, pp 216-227 http://dx.doi.org/10.22436/jmcs.015.03.06

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Authors

Rajib Ghosh - Department of Mathematics, J. K. College, Purulia, West Bengal, 723101, India Ganesh. C. Gorain - Department of Mathematics, J. K. College, Purulia, West Bengal, 723101, India Samarjit Kar - Department of Mathematics, N. I. T, Durgapur, West Bengal, 723209, India

Abstract

In this paper, the asymptotic behaviour of the vibrations of a damped linear string is studied. The exponential stability result of the overall system is obtain directly by means of an exponential energy decay estimate. A closed form approximate numerical result is constructed by fuzzy transform method to support and implement the stability result.

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Keywords

• Uniform stability
• exponential energy decay estimate
• Layapunov function
• fuzzy transform method.

MSC

•  35B35
•  93D05
•  74K05
•  74H45

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