  We consider an undamped nonlinear hinged-hinged beam with stretching
nonlinearity as an infinite dimensional hamiltonian system.
  We obtain analytically a quantitative Birkhoff Normal Form, via a nonlinear
coordinate transformation that allows us to integrate the system up to a small
reminder, providing a very precise description of small amplitude solutions
over large time scales. The optimization of the involved estimates yields
results obtained for realistic values of the physical quantities and of the
perturbation parameter.
