  We present a detailed study of the dynamic response of a ring of $N$ equally
spaced Josephson junctions to a time-periodic external flux, including
screening current effects. The dynamics are described by the resistively
shunted Josephson junction model, appropriate for proximity effect junctions,
and we include Faraday's law for the flux. We find that the time-averaged $I-V$
characteristics show novel {\em subharmonic giant Shapiro voltage resonances},
which strongly depend on having phase slips or not, on $N$, on the inductance
and on the external drive frequency. We include an estimate of the possible
experimental parameters needed to observe these quantized voltage spikes.
