Uniform Stability of a Laminated Beam with Structural Memory

Abstract

Of concern is a structure consisting of two identical beams of uniform thickness. The beams are fastened tightly but still allowing an interfacial slip between the two components. This means that we are in presence of a longitudinal displacement and at the same time keeping a continuous contact of the layers. These beams are also subject to rotatory inertia and shear forces. We prove uniform stability of the system when a viscoelastic damping acts on the effective rotation and in the slip. This extends previous works where boundary controls were used in addition to a frictional damping in the dynamic of the slip.

Well‐posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks

“…For stability of laminated Timoshenko beams with structural memory, one can refer to the previous studies. [23][24][25][26] For laminated Timoshenko beams with second sound, one can find a stability result in Apalara. 27 The delay effects often appears in many practical problems, for instance, chemical, physical, thermal, and economic phenomena, and may turn a well-behaved system into a wild one.…”

Well‐posedness and asymptotic stability to a laminated beam in thermoelasticity of type III

“…and v 2 ∈ H 2 (0, 1) ∩ H 1 0 (0, 1), which gives (9) 6 . Similarly, we get v 3 ∈ H 2 (0, 1) ∩ H 1 0 (0, 1).…”

“…Tatar 5 proved that the system with condition G < I (for D = 1) could be stabilized in an exponential manner using boundary controls. Furthermore, Lo and Tatar 6 investigated uniform stability of the system with damping acting on the effective rotation and in the slip…”

On the Stability of a Laminated Beam With Structural Damping and Gurtin-Pipkin Thermal Law

“…In fact, Cattaneo law (1.5) can be reduced as a particular instance of (1.6), which have been proved in [9]. For other asymptotic behavior results to laminated beams, we refer the reader to [6,12,19,20,21,25,26] and the references therein.…”