On the exponential decay of the Euler-Bernoulli beam with boundary   energy dissipation
  We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the "exponential decay" of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy. 
Barbara Lazzari and Roberta Nibbi
math-ph cs.SY math.MP math.OC