In this paper, we consider a nonlinear beam equation with a strong damping and the $p(x)$-biharmonic operator. The exponent $p(\cdot)$ of nonlinearity is a given function satisfying some condition to be specified. Using Faedo-Galerkin method, the local and global existence of weak solutions is established with mild assumptions on the variable exponent $p(\cdot)$. This work improves and extends many other results in the literature.