The paper is devoted to the dynamics of the model for a beam with strong damping(P ε )ε2utt+εδut+αuxxxx+utxxxx−[g(∫0luξ2dξ)+εσ∫0lutξuξdξ]uxx=0,(x,t)∈]0,l[×]0,∞[, where g:R→R is continuously differentiable, δ,σ∈R and α,l,ε>0, subject to boundary conditions corresponding to hinged or clamped ends.We show that for ε→0+ the dynamics of the equation is close to the dynamics of equation(P 0 )ut=−αu−g(∫0luξ2dξ)A−1/2u, where Au:=uxxxx with the domain determined by one of the above boundary conditions. Specifically, we show that isolated invariant sets of (P 0 ) continue to isolated invariant sets of (P ε ), ε>0 small, having the same Conley index. Moreover, isolated Morse decompositions with respect to (P 0 ) continue to isolated Morse decompositions of (P ε ), ε>0 small, having isomorphic homology index braids.Under some additional assumptions we establish existence and upper semicontinuity results for attractors of (P 0 ) and (P ε ), ε>0 small, extending previous results by Ševčovič.