Horizontally shaken impact pendulums

We consider two pendulum masses attached to the same pivot point and which interact with each other through Hertzian impacts. We show that this splitting of the mass leads to an instability in the conservative case, in which initially synchronized large amplitude motion may evolve into out-of-phase (impacting) motion. We then study in detail the response of the impacting masses in the presence of damping and driving through horizontal shaking of the pivot point. We find that synchronized modes are usually accompanied by small amplitude quasi-periodic, or even chaotic, impacts and a number of multi-period solutions may appear in the bifurcation diagram. We reveal the existence and stability of a number of impact modes and scan the frequency response of the system to a series of initial conditions to identify which modes may be more easily generated in experiment.