Simultaneous boundary control of a Rao-Nakra sandwich beam

We consider the problem of boundary control of a system of three coupled partial differential equations that describe a three layer (Rao-Nakra type) sandwich beam with damping proportional to shear included in the core layer. In the case where one control is applied to each equation, we obtain exact controllablity modulo a finite dimensional quotient in a time determined by the three wave speeds. We show that in a longer time, under some mild conditions on the parameters, we can recover a similar exact controllability result using only two, or possibly even one appropriately chosen control function.