Dynamics of Laminated Timoshenko Beams
- 109 Downloads
This paper is concerned with long-time dynamics of laminated beams modeled from the well established Timoshenko system. Of particular interest is a model of two-layered beam proposed by Hansen and Spies which describes the slip effect produced by a thin adhesive layer uniting the structure. In a more general setting, involving a nonlinear foundation, we establish the existence of smooth finite dimensional global attractors for the corresponding solution semigroup.
KeywordsTimoshenko system Laminated beam Interfacial slip Global attractor Superlinear damping Quasi-stable systems
Mathematics Subject Classification35B41 35L53 74K10
The authors thank the referee for his/her constructive remarks on a previous version of the paper. They also thank the partial support of CNPq (Brazil).
- 13.Hansen, S.W.: A model for a two-layered plate with interfacial slip. In: Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena (Vorau, 1993), pp. 143–170. Birkhauser, Basel (1994)Google Scholar
- 18.Ma, T.F., Monteiro, R.N.: Singular limit and long-time dynamics of Bresse systems. SIAM J. Math. Anal. (to appear)Google Scholar