Built on the V-
一-V reduplication pattern, which softens an action into 'do X for a bit / a little'. Compare
看一看 (kàn yi kàn 'have a look'),
想一想 (xiǎng yi xiǎng 'think it over').
静一静 thus means 'quiet down for a bit' rather than a sharp command. The middle
一 is unstressed: jìng-yi-jìng.