A loud audible alarm may help, but unless it is somehow installed to detect early methods of break-in the doors or windows will still be damaged. A self contained loud audible motion detector type alarm isn't very expensive should you decide that it is worth the effort/cost. Another cheap method is to place burglar alarm warning stickers prominently on the trailer. That can help whether there is really an alarm or not. "Walk like a duck."
As has been said, there is really no way to secure an RV/travel trailer which is stored unoccupied. The unfortunate truth is that the first line of defense for preventing any damage to your RV is the storage facility security measures. Anything else usually stops the entry process after the damage has already occurred. There are few storage areas which have a level of security which will stop a determined band of thieves in an urban area.
I suggest finding a rural area farmer who rents storage space. Nobody likes traveling on country roads with stolen goods. It's a plus if the owner has this sign in his front yard. Your trailer will likely never be at risk.