I have heard some people say that shining and flashing lights at beavers around there lodge they will leave. This might cause a temporary solution but animals can get use to that. Mostly beaver like a quiet and calm surrounding but these methods will only work if the beaver are first thinking of moving in to the area.
The only real and permanent solution to beavers or beaver damage is the removal of the beaver and management program to contain there numbers and damage. When beaver are in a certain area mostly likely every year or two different beaver will come back to that area. So set up a management plan with a Wildlife Control Operator.