A classical approach to uniform null controllability for elastic beams

The Rayleigh beam equation is the formal limit of the Timoshenko beam equation as the shear modulus K→+∞. Null controllability is possible, that is, the evolution systems associated with the Rayleigh and Timoshenko equations can be driven to rest by applying appropriate controls at both ends of the beam. In this work we show that controllability of the Rayleigh system can be achieved by letting K→+∞ in the solution of the Timoshenko controllability problem