In this paper, we deal with the elastic vibrations of flexible structures modeled by the ‘standard linear model’ of viscoelasticity in n-dimensional space. We study the uniform exponential stabilization of such kind of vibrations after incorporating separately very small amount of passive viscous damping and internal material damping of Kelvin-Viogt type in the model. Explicit forms of exponential energy decay rates are obtained by a direct method, for the solution of such boundary value problems without having to introduce any boundary feedback.
Gorain, Ganesh C.
Uniform Stabilization of n-Dimensional Vibrating Equation Modeling ‘Standard Linear Model’ of Viscoelasticity,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 4,
2, Article 7.
Available at: https://digitalcommons.pvamu.edu/aam/vol4/iss2/7