In this paper we study the phenomenon of nonlinear supratransmission in a
semi-infinite discrete chain of coupled oscillators described by modified
sine-Gordon equations with constant external and internal damping, and subject
to harmonic external driving at the end. We develop a consistent and
conditionally stable finite-difference scheme in order to analyze the effect of
damping in the amount of energy injected in the chain of oscillators; numerical
bifurcation analyses to determine the dependence of the amplitude at which
supratransmission first occurs with respect to the frequency of the driving
oscillator are carried out in order to show the consequences of damping on
harmonic phonon quenching and the delay of appearance of critical amplitude.