Are you sure your an extrovert ALL the time? Why is that you are afraid to show your enthusiam/eye contact to his friends? Nothing wrong with being shy sometimes, I am around new people but gradually come out of my shell the more time I spend around that person. It sometimes helps if you know something about them and can chat about that...like their favorite sports team or movie or whatever. Just throw something out there after the introductions, something you are comfortable talking about and it will be easy.
Just relax and try to remember that everyone is human and they want to meet you.
So, so you think you can tell Heaven from Hell,
blue skies from pain.
Can you tell a green field from a cold steel rail?
A smile from a veil?
Do you think you can tell?
And did they get you to trade your heroes for ghosts?
Hot ashes for trees?
Hot air for a cool breeze?
Cold comfort for change?
And did you exchange a walk on part in the war for a lead role in a cage?