I agree, you have to leave the child in the napping place until 'nap time' is over. They will eventually get it.
Im trying to think, if at 11 months, if they would normally have one or two naps a day. If you want to give two naps, put them each down after a snack or bottle for an hour to an hour and a half in the morning, then again in the afternoon. Stick with setting a strong schedule. Put them down the same time everyday if possible.
Here I have young ones, (17 mos) and they all go down for one nap for 2.5 hrs and naptime is right after lunch. The know when naptime is coming and they all fall asleep without a peep.
I have been watching them since they were 12 months and since then we more or less stuck with one long nap each day right after lunch.
It may have took 1-2 weeks for my full timer to get the idea and go down without protest, and maybe 3 weeks for my part-timer to 'get-it'.
It is your responsibility to not give in and leave them be to cry-it-out. They WILL eventually learn to sleep on their own, and they will be much happier and healthier because of it.