Exponential stability of a joint-leg-beam system with memory damping

In this paper, we consider a system for combined axial and ransverse motions of two viscoelastic Euler-Bernoulli beams connected through two legs to a joint. This model comes from rigidizable and inatable space structures. First, the exponential stability of the joint-leg-beam system is obtained when both beams are subject to viscoelastic damping and memory kernels satisfy reasonable assumptions. Then, we show the lack of uniform decay of the coupled system when only one beam is assumed to have a memory damping and the second beam has no damping.