Dynamical elastic contact of a rope with the ground

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 governed by an infinite set of linear nonlinear resonances. In limit weak bending stiffness, fundamental frequency found be independent tension. transition between radiation-less wave radiating state occurs via series grazing bifurcations, whereby new contacts are formed. bifurcations form overlapping Arnold tongues in frequency-amplitude parameter space. Finally, for ropes large stiffness when geometric nonlinearity important, bistability observed several wave-making regimes.