Exact boundary controllability of a Rao-Nakra sandwich beam

Scott W. Hansen, Rajeev Rajaram, Ralph C. Smith
2005 Smart Structures and Materials 2005: Modeling, Signal Processing, and Control  
We consider a three layer Rao-Nakra sandwich beam with damping proportional to shear included in the core layer. We prove that eigenvectors of the beam form a Riesz basis for the natural energy space. In the damped case, we are able to give precise conditions under which solutions decay at a uniform exponential rate. 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
more » ... finite co-dimension and provide sufficient conditions (related to small damping) for exact controllability to a zero energy state. The boundary control functions acting at the right end of the beam are M (t), the applied moment, and g O (t) = (g 1 (t), g 3 (t)) T , the longitudinal force. Our main result is the following: Theorem 1. The eigenvectors associated with (1), (2) form a Riesz basis for the finite energy space X 0 × X 1 .
doi:10.1117/12.598258 fatcat:7qotbrqkefaxfiskbu65aj26ai