Energy decay results for some laminated beams with memory

Abstract

In this article, we investigate two systems of laminated beams with memory effects. It is well-known that such a system with a single
dissipation mechanism lacks exponential decay unless another damping mechanism is added. In contrary, we prove that a unique
dissipation given by the memory term, acting on the effective rotation or in the slip, is strong enough to stabilize the system
exponentially, depending on the kernel of the memory effects and the wave speeds of the system. In fact, we prove a general decay result
for the two systems, for which exponential and polynomial decay results are special cases. This result is new and improves earlier
results in the literature.