Check the headset to make sure it has no play, to make sure that isn't vibrating.
Adjust the brake calipers to eliminate play in both arms. Play in the pivots can cause a vibration which leads to shudder. Tighten the pivots till they start to bind slightly, test the bike. If the shudder goes away, its the calipers. Loosen them to just the point where they no longer bind.
Il faut de l'audace, encore de l'audace, toujours de l'audace
1980 3Rensho-- 1975 Raleigh Sprite 3spd
1990s Raleigh M20 MTB--2007 Windsor Hour (track)
1988 Ducati 750 F1