Electron. J. Diff. Equ., Vol. 2015 (2015), No. 129, pp. 1-14.

Stabilization of laminated beams with interfacial slip

Assane Lo, Nasser-eddine Tatar

We study a laminated beam consisting of two identical beams of uniform thickness, which is modeled as Timoshenko beams. An adhesive of small thickness is bonding the two layers and creating a restoring force producing a damping. It has been shown that the interfacial slip between the layers alone is not enough to stabilize the system exponentially to its equilibrium state. Some boundary control has been used in the literature for that purpose. In this paper, we show that for viscoelastic material there is no need for any kind of internal or boundary control.

Submitted February 24, 2015. Published May 7, 2015.
Math Subject Classifications: 34B05, 34D05, 34H05.
Key Words: Exponential stabilization; vibration reduction; Timoshenko system; slip; boundary control; multiplier technique.

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Assane Lo
University of wollongong in Dubai
Dubai, UAE
email: assanelo@uowdubai.ac.ae
Nasser-eddine Tatar
King Fahd University of Petroleum and Minerals
Department of Mathematics and Statistics
Dhahran 31261, Saudi Arabia
email: tatarn@kfupm.edu.sa

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