The title asks it all.
The small rugs are no big problem, but we've gone thru a number of the
longer rubber backed mats (garage entrance, for wet shoes and boots) that
have seemed to shred along an edge. I believe its from the whipping action.
I also suspect that vacuuming them is as effective. Sure, catching the edge
(getting sucked/caught in the vacuum) can be tricky, but I've got a
technique worked out that eliminates that.
My wife says shaking is the only way.