On initial conditions for a boundary stabilized hybrid Euler-Bernoulli beam

Bose, Sujit K. (2001) On initial conditions for a boundary stabilized hybrid Euler-Bernoulli beam Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 111 (3). pp. 365-370. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/mathsci/vol111/aug2001/pm-183...

Related URL: http://dx.doi.org/10.1007/BF02829602

Abstract

We consider here small flexural vibrations of an Euler-Bernoulli beam with a lumped mass at one end subject to viscous damping force while the other end is free and the system is set to motion with initial displacement y0(x) and initial velocity y1(x). By investigating the evolution of the motion by Laplace transform, it is proved (in dimensionless units of length and time) that ∫01y2xtdx ≤ ∫01y2xxdx,t > t0, where t0 may be sufficiently large, provided that {y0,y1} satisfy very general restrictions stated in the concluding theorem. This supplies the restrictions for uniform exponential energy decay for stabilization of the beam considered in a recent paper.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Euler-bernoulli Beam Equation; Hybrid System; Initial Conditions; Small Deflection; Exponential Energy Decay
ID Code:6267
Deposited On:20 Oct 2010 11:21
Last Modified:16 May 2016 16:36

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