Asymptotic stability of solutions to elastic systems with structural damping. (English) Zbl 1315.35034
Summary: In this article, we study the asymptotic stability of solutions for the initial value problems of second order evolution equations in Banach spaces, which can model elastic systems with structural damping. The discussion is based on exponentially stable semigroups theory. Applications to the vibration equation of elastic beams with structural damping are also considered.
MSC:
35B40 | Asymptotic behavior of solutions to PDEs |
47D03 | Groups and semigroups of linear operators |
35L90 | Abstract hyperbolic equations |
74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
74H45 | Vibrations in dynamical problems in solid mechanics |