  We consider a heavy, uniform, elastic beam rested on periodically distributed
supports as a simplified model of a bridge. The supports are subjected to a
partial destruction propagating as a failure wave along the beam. Three related
models are examined and compared: (a) a uniform elastic beam on a distributed
elastic foundation, (b) an elastic beam which mass is concentrated at a
discrete set of points corresponding to the discrete set of the elastic
supports and (c) a uniform elastic beam on a set of discrete elastic supports.
Stiffness of the support is assumed to drop when the stress reaches a critical
value. In the formulation, it is also assumed that, at the moment of the
support damage, the value of the `added mass', which reflects the dynamic
response of the support, is dropped too. Strong similarities in the behavior of
the continuous and discrete-continuous models are detected. Three speed
regimes, subsonic, intersonic and supersonic, where the failure wave is or is
not accompanied by elastic waves excited by the moving jump in the support
stiffness, are considered and related characteristic speeds are determined.
With respect to these continuous and discrete-continuous models, the conditions
are found for the failure wave to exists, to propagate uniformly or to
accelerate. It is also found that such beam-related transition wave can
propagate steadily only at the intersonic speeds. It is remarkable that the
steady-state speed appears to decrease as the jump of the stiffness increases.
