Synchronous rotational motion of parametric pendulums

• We study theoretically and experimentally the synchronization of rotating parametric pendulums.
• Different modes of synchronized pendulum responses have been observed.
• Rotations of pendulums in antiphase damp of the horizontal vibration in the base.
• Synchronization of pendulums in antiphase is more beneficial for sustaining rotation.
• Synchronized rotation is preserved in the presence of noise or parameter mismatch.

We study theoretically and experimentally the synchronization phenomenon of two rotating parametric pendulums attached to common elastic support under harmonic excitation. Two types of synchronous states have been identified – complete and phase synchronization. The interactions in the system have been investigated numerically and experimentally. The relation between the synchronization mode and the stability of the rotational motion for a system with flexible support has been studied. It has been demonstrated that the synchronization of pendulums rotating in antiphase is more beneficial from energy harvesting viewpoint than the synchronization in phase. Finally, an influence of the parameter mismatch between the pendulums on their synchronization has been examined.