  In this paper, we consider two systems of type Rao-Nakra sandwich beam in the
whole line R with a frictional damping or an infinite memory acting on the
Euler-Bernoulli equation. When the speeds of propagation of the two wave
equations are equal, we show that the solutions do not converge to zero when
time goes to infinity. In the reverse situation, we prove some L2(R)-norm and
L1(R)-norm decay estimates of solutions and theirs higher order derivatives
with respect to the space variable. Thanks to interpolation inequalities and
Carlson inequality, these L2(R)-norm and L1(R)-norm decay estimates lead to
similar ones in the Lq(R)-norm, for any q>1. In our both L2(R)-norm and
L1(R)-norm decay estimates, we specify the decay rates in terms of the
regularity of the initial data and the nature of the control.
