  We consider a non acoustic chain of harmonic oscillators with the dynamics
perturbed by a random local exchange of momentum, such that energy and momentum
are conserved. The macroscopic limits of the energy density, momentum and the
curvature (or bending) of the chain satisfy a system of evolution equations}.
We prove that, in a diffusive space-time scaling, the curvature and momentum
evolve following a linear system that corresponds to a damped Euler-Bernoulli
beam equation. The macroscopic energy density evolves following a non linear
diffusive equation. In particular the energy transfer is diffusive in this
dynamics. This provides a first rigorous example of a normal diffusion of
energy in a one dimensional dynamics that conserves the momentum.
