  A rope laid on the ground with one end subjected to time-dependent forcing is
proposed as a prototypical elastic dynamical contact problem, which we study
analytically, numerically, and experimentally. The dynamics is governed by an
infinite set of linear and nonlinear resonances. In the limit of weak bending
stiffness, the fundamental frequency is found to be independent of the rope
tension. A transition between a radiation-less and a wave radiating state
occurs via a series of grazing bifurcations, whereby new contacts between the
rope and the ground are formed. The grazing bifurcations form overlapping
Arnold tongues in the frequency-amplitude parameter space. Finally, for ropes
with large bending stiffness and when the geometric nonlinearity is important,
bistability is observed between several wave-making regimes.
