  We consider an abstract nonlinear second order evolution equation, inspired
by some models for damped oscillations of a beam subject to external loads or
magnetic fields, and shaken by a transversal force. When there is no external
force, the system has three stationary positions, two stable and one unstable,
and all solutions are asymptotic for $t$ large to one of these stationary
solutions.We show that this pattern extends to the case where the external
force is bounded and small enough, in the sense that solutions can exhibit only
three different asymptotic behaviors.
