Meson cannon does not burn out shields. So any hit has its damage reduced by the shields, but shields don't go down.
Example:
A Hazat Adonais drednought fires its meson cannon at a Li Halan Dragon destroyer.
Meson Cannon: 1AD Devastating +2, multihit 36d.
Dragon: Hull 5, 4 shields, 30 damage.
Rolls one dice - a bit hit or miss!
The dreadnought' player throws 5 - a hit!
Because the cannon is multi-hit 3d6, he rolls 4,3,6 - inflicting 13 hits. The Dragon's shields stop 4 of those hits, but shields are not reduced. 9 hits are now rolled, on the attack table.
1,1,2,3,4,5,5,6,6 - which gives 2 bulkhead hits, and 2 criticals, for 7 damage plus crits.
Crits are: 1 & 4 - but because they are devastating +2, they are level 3 crits. 14 extra damage and a whole load of other problems, including a level 1 crew crit for another damage.
The destroyer is left on 8 damage and crippled. But it still has full shields!