Uniform Stability of a Laminated Beam with Structural Memory

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.