Onset instability of a parametrically excited pendulum array

In the theoretical framework of the Floquet instability analysis we have investigated the onset instability of the one-dimensional pendulum array, a macroscopic expression of the Frenkel-Kontorova chain, subjected to vertical vibration after the continuum approximation. The Floquet instability calculation shows that the onset instability of the array always responds to the forcing frequency subharmonically. The theoretical predictions of the critical forcing conditions and onset instability waves have been validated by experiments. Good agreement between the theoretical calculations and experimental observations has been achieved for the onset instabilities with both long and short wavelengths.