Exponential Stabilization of an Euler-Bernoulli Beam with a Tip Body Using Strain Feedback

Abstract

For motor controlled Euler-Bernoulli beam without a tip body, it has been shown that strain feedback can exponentially stabilize the whole system. On the other hand, it is observed in the existing literature that the exponential stability may no longer hold under boundary velocity feedbacks if the beam is fitted with a tip body. So care must be taken in dealing with equations of beam with tip body. It is thus the purpose of this paper to investigate the exponential stability of the strain feedback controlled dynamic equation of an Euler-Bernoulli beam with a tip body. The energy multiplier method is employed in proving the main theorem in which a key point is to choose an appropriate multiplier.