The voltage induced in a coil, say for example the primary of a transformer, is proportional to the rate at which the current is changing. For most of the systems we deal with, the current varies from max positive to max negative and back again 60 times every second. That is the "rate of change of current" that would create a voltage in the primary of a transformer.
But for the most part, "DC" current does not change. Its "Rate of Change" is zero. So the voltage it would create in the primary windings would also be zero. That would mean that there is nothing available to induce a voltage in the secondary. Thus, the secondary voltage would be zero. Thus, you don't get an AC waveform out, when your input is DC. What you get as an output is zero volts, and zero current.