Boundary feedback stabilization of the undamped Euler-Bernoulli beam with both ends free

In this paper, we are concerned with a boundary feedback system of a class of nonuniform undamped Euler-Bernoulli beam with both ends free. We give some sufficient conditions and some necessary conditions for the system to have exponential stability. Our method is based on the operator semigroup technique, the multiplier technique, and the contradiction argument of the frequency domain method.