Block an IP Address

I am the Systems Admin for a non-profit school. I have some students or faculty that are placing thier computers on the network. We are not stopping this, but they are setting tier IP Address in the DHCP Range. Every day they change thier addressto impact someone else. I refuse to change my range and would like to know if there is a way to bump that person off the network. Our network is flat. I do not have any equipment to speak of to assist. Just me.

Any help would be great

Jack