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We consider the Euler-Bernoulli beam equation with a local Kelvin-Voigtdissipation type in the interval $(-1,1)$. The coefficient damping is onlyeffective in $(0,1)$ and is degenerating near the $0$ point with a speed atleast equal to $x^{\alpha}$ where $\alpha\in(0,5)$. We prove that the semigroupcorresponding to the system is polynomially stable and the decay rate dependson the degeneracy speed $\alpha$.

Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping