  Bending vibrations of thin beams and plates may be described by nonlinear
Euler-Bernoulli beam equations with $x$-dependent coefficients. In this paper
we investigate existence of families of time-periodic solutions to such a model
using Lyapunov-Schmidt reduction and a differentiable Nash-Moser iteration
scheme. The results hold for all parameters $(\epsilon,\omega)$ in a Cantor set
with asymptotically full measure as $\epsilon\rightarrow0$.
