This question Is really hard to answer. So I can only give pointers and take what you may from It and disregard what you want.
Playing AK, depends mainly on many factors.
A) The position your In, Isn't as Important as the player you're up against. This doesn't mean that you should go "Ham" wtih AK vs a "Rock/Nit" Just because It's "AK" (I hope you understand). You state that you "3bet" with AK, so the question than becomes "How much does your 3bet size look like", and "Whom you're 3betting vs"?
B) You need to understand, that not all players play alike. Once you understand this notion than you'll understand better how to better play AK, vs different villains, since not all villains have the same tendencies and some fold to Cbets alot higher percentage of the time, while others are more "Sticky" post-flop, and some are "Outright Insane". So you need to Adjust, how to play vs the different player types. If the raiser Is a Maniac, there are different avenues/roads/choices you can take. You can 3bet OOP (knowing full well that he/she might Just pile It In, for 100+BBs cash/tourney), B) Flat to keep the pot small and see exactly how they act post-flop and/or get another player to attempt to (Either Iso, the "Maniac and/or You"), In which case you than can (Pile It In, and/or call OOP still or 4bet/Re-Raise).
C) Just because you have AK on a wet board doesn't mean you need to bet. You need to understand this concept, the Cbet Is only meant to work vs certain player types, and "Value Bets" work vs "Certain player types". So with that said, you aren't ever gonna get a "Passive Calling Station" of've TPQK on a 10 high board when they're holding 10/Qo because realistically speaking these players don't "Think", they Just see "Their cards" and don't care about bets/ranges/Images. So by betting Into them, and seeing them "Calling you", what In the world are you than trying to do? As you only leave yourself with one option on the river and that's "All In", correct? Than you complain about how "Terrible you run", or how It was such an "Awful call"? Re-examine your play, and work out where you went wrong, will work wonders and help you come a long way Into your poker game
Again, too many variables to really get an In-depth answer to "What should I do If flop Is dry" really depends on player? Their "Fold to Cbet %", the "Type of player", are you "In Position", are you "OOP", what Is the "Stack depth/BB's remaining", are you "On the bubble of a tourney", If so "How many players are shorter than you".
I can't really answer all so unless you post an example (Without the results), than I can better help answer the question