Supratransmission in transversely connected nonlinear pendulum pairs

Abstract

In this work, we generate a nonlinear supratransmission phenomenon in a chain of coupled pendulum pairs, where each pendulum is connected to the nearest neighbours in the longitudinal and transverse directions. By considering the angular displacement of one chain proportional to the other, we derive the homoclinic supratransmission threshold amplitude using the two-dimensional map approach which is in agreement with the numerical one; in the case where only one chain is driven. We also consider the case where both chains are driven and perform numerically the supratransmission threshold amplitude of the two chains in the case of the same driven frequency while the phonon amplification is obtained when both lattices are driven with frequencies in different bands. The actual work extends the deep understanding of supratransmission phenomenon in discrete coupled pendulum systems.