  We study the boundary controllability problem for a multilayer Rao-Nakra
sandwich beam. This beam model consists of a Rayleigh beam coupled with a
number of wave equations. We consider all combinations of clamped and hinged
boundary conditions with the control applied to either the moment or the
rotation angle at an end of the beam. We prove that exact controllability holds
provided the damping parameter is sufficiently small. In the undamped case,
exact controllability holds without any restriction on the parameters in the
system. In each case, optimal control time is obtained in the space of optimal
regularity for $L^2(0,T)$ controls. A key step in the proof of our main result
is the proof of uniqueness of the zero solution of the eigensystem with the
homogeneous boundary conditions together with zero boundary observation.
