Modeling and boundary stabilization of a multiple beam system

In this paper we consider two mathematical models for a multiple beam system (MBS) which is composed of two rigidly and angularly connected Euler-Bernoulli beams The cantilevered structure is clamped at one end, and has point controls for forces and bending moments imposed at the other end and at the connection between the two beams The first model incorporates not only transverse deformations of both beams, but also axial compression/extension of the beams. The second model involves only transverse deformations of the beam. By imposing point controls, an unbounded input operator is obtained A variational formulation of the models is used to show well-posedness. Uniform exponential stabilizability of the second model through boundary feedback is established via energy arguments