Do wires with DC current vibrate like wires with AC current (very tiny vibrations)? Do wires with DC current vibrate like wires with AC current (very tiny vibrations)?
 A: Wires with DC current do not vibrate. In the cases of AC you have currents moving through the wires that are constantly changing direction. Because currents create magnetic fields, electrical wires will move back and forth, or vibrate due to these changing magnetic fields.
A: I am just adding to what Dr. jh says - but am adding as an answer so i can show the video below.  The magnetic force between two parallel conductors carrying current is,
$$\frac{F}{l} = \frac{\mu_0 I_1I_2}{2\pi r}$$
in N/m where r is the distance between the two conductors.
Below i show the two AC current waveforms as they go from being in-phase to 180° out-of-phase (both have magnitude of 10A peak) and r = 5 meters.  F/l is in μN/m so it shows up on this scale (notice it is twice the frequency of the currents).

This Lorentz force can actually cause problems with utility transmission line protective relaying.  Quoting from Cigre B5.47 Network protection performance audits: "Real fault cases show that bundled conductor contractions which occur as a result of the Lorentz forces associated with high fault currents can influence the reactance measurements of distance protection relays. The contractions cause an increase in the line reactance and this can lead to an underreach of distance protection relays during actual three phase faults."
