Abstract
In this paper, we consider an Euler–Bernoulli beam equation with one segment of the beam made of viscoelastic material of Boltzmann type and the other segment made of elastic material. Strong stability and exponential stability of the associated semigroup are obtained under certain smoothness conditions imposed on the coefficient functions of the equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F.L. Huang, Strong asymptotic stability of linear dynamical systems in Banach spaces. J. Diff. Equations 104 (1985) 307–324.
F.L. Huang, Characteristic condition for exponential stability of linear dynamical systems in Hilbert spaces. Ann. Diff. Equations 1(1) (1985) 43–56.
K. Liu and Z. Liu, Exponential decay of energy of the Euler-Bernoulli beam with locally distributed Kelvin-Voigt damping. SIAM J. Control Optim. 36(3) (1998) 1086–1098.
K. Liu and Z. Liu, Exponential decay of energy of vibrating strings with local viscoelasticity. Z. Angew Math. Phys. 53 (2002) 265–280.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983).
J.E.M. Rivera and A.P. Salvatierra, Asymptotic behaviour of the energy in partially vsicoelastic materials. Quart. Appl. Math. LIX(3) (2001) 557–578.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhao, H., Liu, K. & Liu, Z. A Note on the Exponential Decay of Energy of a Euler–Bernoulli Beam with Local Viscoelasticity. Journal of Elasticity 74, 175–183 (2004). https://doi.org/10.1023/B:ELAS.0000033863.20719.e2
Issue Date:
DOI: https://doi.org/10.1023/B:ELAS.0000033863.20719.e2