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Riesz basis property and related results for a Rao-Nakra sandwich beam
We consider a three layer Rao-Nakra sandwich beam with distinct wave speeds.
We prove that the eigenvectors form a Riesz basis for the natural
energy space. In the damped case, we give precise conditions under which
there is a uniform exponential decay of energy. We also consider the
problem of boundary control using bending moment and lateral force control
at one end. We prove that the space of exact controllability has finite co-dimension and
provide sufficient conditions (related to small damping) for exact
controllability to a zero energy state.