This paper deals with a dynamic Euler-Bernoulli beam of infinite length subjected to a moving concentrated Dirac mass. The beam relies on a foundation composed of a continuous distribution of linear elastic springs associated in parallel with a uniform distribution of Coulomb friction elements and viscous dampers. The problem is stated in distributional form, and the existence and uniqueness results are established by means of a combination of $ {\rm{ L}} ^\infty$–$ {\rm{L}}^2 $–$ {\rm{L }}^1$ estimates together with a monotonicity argument. Traveling wave solutions are studied in detail in the case without Coulomb friction, and they are shown to be globally exponentially stable under positive viscous damping.