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Abstract. We consider the synchronization of two self-excited double pendula. We show that such pendula hanging on the same beam can have four different synchronous configurations. Our approximate analytical analysis allows us to derive the synchronization conditions and explain the observed types of synchronization. We consider an energy balance in the system and describe how the energy is transferred between the pendula via the oscillating beam, allowing thus the pendula synchronization. Changes and stability ranges of the obtained solutions with increasing and decreasing masses of the pendula are shown using path-following.

We consider the synchronization of n self-excited double pendula. For such pendula hanging on the same beam, different synchronous configurations can be obtained (in-phase and anti-phase states). An approximate analytical analysis allows to derive the synchronization condition and explain the observed types of synchronization for any number of coupled double pendula. The energy balance method is used to show how the energy between the pendula is transferred via the oscillating beam allowing their synchronization. We compute periodic solutions for n = 2, 3, 4, 5 coupled double pendula, based on analytical predictions. For all obtained periodic solutions, we investigate how the stability properties change with the varying natural frequency of the beam.