Exact boundary controllability of two Euler-Bernoulli beams connected by a point mass
We consider a hybrid system consisting of two flexible beams connected by a point mass. In a previous work, we showed that when the constant of rotational inertia gamma is positive, due to the presence of the mass, the system is well posed in asymmetric spaces, i.e., spaces with different regularity to both sides of the mass. As a consequence of this, the space of controllable data when we act on the free extreme of the system is also an asymmetric space when gamma > 0. In this paper, we study the case gamma = 0 in which we recover the classical Euler-Bernoulli model for the beams. We prove in this case that the system is not well posed in asymmetric spaces and then the presence of the point mass does not affect the controllability of the system. The proofs are based in the development of solutions in Fourier series and the use of nonharmonic Fourier series. (C) 2000 Elsevier Science Ltd. All rights reserved.
controllability point mass flexible beams fourier series