The limiting behavior of global attractors ${𝒜}_{\epsilon }$ for singularly perturbed beam equations $${\epsilon }^2\frac{{\partial }^{2}u}{\partial t^2}+\epsilon \delta \frac{\partial u}{\partial t}+A\frac{\partial u}{\partial t}+\alpha Au+{g(\parallel u\parallel }_{1/4}^2)A^{1/2}u=0$$ is investigated. It is shown that for any neighborhood $𝒰$ of ${𝒜}_0$ the set ${𝒜}_{\epsilon }$ is included in $𝒰$ for $\epsilon$ small.