We study the Riesz basis property and the stability of a flexible Euler-Bernoulli beam, that is, clamped at one end and is free at the other. To stabilize the system, we apply a boundary control force in position and velocity at the free end of the beam. We first prove the well-posedness of the closed-loop system and then analyze the spectrum of the system. Using Shkalikov’s method, we obtain the Riesz basis property. The spectrum determined growth condition and the exponential stability are also concluded.

beam equation, semigroup theory, asymptotic analysis, Riesz basis, exponential stability.