Stabilization for the vibrations modeled by the `standard linear model' of viscoelasticity

Author： Gorain Ganesh  

Publisher： Springer Publishing Company

ISSN： 0253-4142

Source： Proceedings Mathematical Sciences, Vol.120, Iss.4, 2010-09, pp. : 495-506

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Abstract

We study the stabilization of vibrations of a flexible structure modeled by the `standard linear model' of viscoelasticity in a bounded domain in ℜ n with a smooth boundary. We prove that amplitude of the vibrations remains bounded in the sense of a suitable norm in a space $$ mathbb{X} $$ , defined explicitly in (22) subject to a restriction on the uncertain disturbing forces on $$ mathbb{X} $$ . We also estimate the total energy of the system over time interval [0, T] for any T > 0, with a tolerance level of the disturbances. Finally, when the input disturbances are insignificant, uniform exponential stabilization is obtained and an explicit form for the energy decay rate is derived. These results are achieved by a direct method under undamped mixed boundary conditions.

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