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In this paper, we focus on the class of almost-periodically forced higher-dimensional beam equations $$ u_{tt}+(-\Delta +\mu )^{2}u+\psi (\omega t)u=0,\quad \mu >0, t \in \mathbb{R}, x\in \mathbb{R}^{d}, $$ subject to periodic boundary conditions, where $\psi (\omega t)$ is real analytic and almost-periodic in t. We show the existence of almost-periodic solutions for this equation under some suitable hypotheses. In the proof, we improve the KAM iteration to deal with the infinite-dimensional frequency $\omega =(\omega _{1},\omega _{2},\ldots)$.

Invariant tori of full dimension for higher-dimensional beam equations with almost-periodic forcing