In this paper, we discussed the asymptotic behavior of the solutions to the beam equation with rotational inertia and structural damping:

$$\epsilon (t)(1+(-\mathrm{\Delta }{)}^{\alpha }){\mathrm{\partial }}_t^{2}u+{\mathrm{\Delta }}^{2}u+\gamma (-\mathrm{\Delta }{)}^{\theta }{\mathrm{\partial }}_{t}u+f(u)=g(x),$$

where $\epsilon (t)$ was a decreasing bounded function. We found a more optimized subcritical exponent $p^{\ast }=\frac{N+2\theta }{N-4}$ depending on $\theta .$ Additionally, we showed that when the growth exponent $p$ of nonlinear terms $f(u)$ was within the range $1⩽p<p^{\ast },$ the well-posedness and regularity were established. Finally, within the theory of process on time-dependent spaces, we investigated the existence of the time-dependent attractor by using the contraction function method and more detailed estimates in the time-dependent space ${\mathcal{H}}_t^{\alpha }.$ The results refined and extended the model and the work in literature [Longtime behavior for an extensible beam equation with rotational inertia and structural nonlinear damping, J. Math. Anal. Appl., 496 (2021), 124785.] from general energy space to time-dependent space in some sense.