Boundary feedback stabilization of a Rao-Nakra sandwich beam

In this paper, we study the boundary feedback stabilization of a three-layer Rao-Nakra sandwich beam. Since we found a proper state space so that the energy of the system is dissipative. We then convert the beam system to an abstract first-order evolution equation with operator A. Afterwards, we obtain A is the infinitesimal generator of a C ₀ – semigroup of contractions by using semigroup theory. The boundary damping makes the system is stable of order 1/2, which is proved by using the frequency domain characterization of polynomial stability. (paper)