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This paper is devoted to initial-boundary value problem of an extensible beamequation with degenerate nonlocal energy damping in$\Omega\subset\mathbb{R}^n$: $u_{tt}-\kappa\Delta u+\Delta^2u-\gamma(\Vert\Delta u\Vert^2+\Vert u_t\Vert^2)^q\Delta u_t+f(u)=0$. We prove the globalexistence and uniqueness of weak solutions, which gives a positive answer to anopen question in [24]. Moreover, we establish the existence of a strongattractor for the corresponding weak solution semigroup, where the ``strong"means that the compactness and attractiveness of the attractor are in thetopology of a stronger space $\mathcal{H}_{\frac{1}{q}}$.

Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping