  We explore the energy decay properties related to a model in extensible beams
with the so-called energy damping. We investigate the influence of the
nonloncal damping coefficient in the stability of the model. We prove, for the
first time, that the corresponding energy functional is squeezed by
polynomial-like functions involving the power of the damping coefficient, which
arises intrinsically from the Balakrishnan-Taylor beam models. As a
consequence, it is shown that such models with nonlocal energy damping are
never exponentially stable in its essence.
