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

Dynamical elastic contact of a rope with the ground