On the control of networks of vibrating strings and beams

Abstract

The authors introduce nonlinear equations describing the vibrations in space of networks of elastic strings and beams. Linearization about an equilibrium configuration yields a hyperbolic system of linear equations coupled by conditions at the multiple nodes where several network members meet. The authors study the controllability of these systems by controls exercised at some nodes. The multiplier method yields a priori inequalities guaranteeing exact controllability, and hence stabilizability, for certain rudimentary networks.<>