  We prove the existence of small amplitude periodic solutions, for a large
Lebesgue measure set of frequencies, in the nonlinear beam equation with a weak
quadratic and velocity dependent nonlinearity and with Dirichlet boundary
conditions. Such nonlinear PDE can be regarded as a simple model describing
oscillations of flexible structures like suspension bridges in presence of an
uniform wind flow. The periodic solutions are explicitly constructed by means
of a perturbative expansion which can be considered the analogue of the
Lindstedt series expansion for the invariant tori in classical mechanics. The
periodic solutions are not analytic but defined only in a Cantor set, and
resummation techniques of divergent powers series are used in order to control
the small divisors problem.
