A Note on Stability of Longitudinal Vibrations of an Inhomogeneous Beam - Applied Mathematics

AM > Vol.3 No.1, January 2012

Applied Mathematics

Volume 3, Issue 1 (January 2012)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

A Note on Stability of Longitudinal Vibrations of an Inhomogeneous Beam ()

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DOI: 10.4236/am.2012.31003 5,087 Downloads 8,999 Views Citations

Author(s)

Prasanta Kumar Nandi, Ganesh Chandra Gorain, Samarjit Kar

Affiliation(s)

ABSTRACT

In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total energy of the system at any time t. By constructing suitable Lyapunov functional, it is established directly that the energy of this system decays exponentially.

KEYWORDS

Inhomogeneous Beam; Longitudinal Vibrations; Uniform Stabilization; Energy Decay Estimate

Share and Cite:

P. Nandi, G. Gorain and S. Kar, "A Note on Stability of Longitudinal Vibrations of an Inhomogeneous Beam," Applied Mathematics, Vol. 3 No. 1, 2012, pp. 19-23. doi: 10.4236/am.2012.31003.

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