Should be an option under the alarm to set the vibrate.
Goto your alarm area. touch the time for the alarm and you should get a menu of options....the ability to turn on/off vibrate as well as the ability to set what is played for the alarm should be here.

Plus I love the option to set the backup beep if the normal alarm plays for too long lol.

 

This very thing happened to me this morning. I had to power off my phone.

I thought it was an isolated incident



Btw, I did have the phone all the way down (volume) and have the option selected for alarm on silence mode

 

sorry thong. its not a setting issue ...the alarm task is bugging out...I had this problem past few days after a fresh factory reset....
to anyone having the issue stated above... navigate your way to the application. settings for the alarm... and wipe its data... try to kill the task in the same window also.... see if that fixes it for you...
so far, so good for me.
this is similar to the fix for the map/gallery glitch...where the gallery refuses to open because the maps app has some glitchy gfx somewhere.
sorry for sloppy message...obviously the alarm worked right if im up this early. everyone with this problem...let me know if it worked for you