How to have the alarm audible when on vibrate or silent?
Are you using the stock Clock application? If so, have you unchecked "Vibrate" from the alarm settings? 


Go to the stock Clock application.
Select the (leftmost) alarm tab in order to configure or add new alarms. 
Uncheck "Vibrate."


This should solve the problem. I have the same device, which I usually keep in silent mode, and my alarm is audible.

As a side note, you could put the device in Airplane mode at night so that texts/calls don't come in. Either way, the alarm will still sound normally.