Moment approach to the boundary exact controllability of an active constrained layer beam

Using the moment approach, we consider the boundary exact controllability of an active constrained layer (ACL) beam consisting of three layers, which is modeled as a Rayleigh beam coupled with two wave equations. We convert the controllability problem of the ACL beam into a corresponding moment problem which can be solvable in a Hilbert space ℓ². Then, we conclude that the ACL beam is exactly controllable when the control time is greater than the maximum value among of the optical lengths of the two waves and the square root of the moment of inertia of the Rayleigh beam. The well-posedness and asymptotic spectral expressions of the ACL beam are also presented.