While I'm not a physics expert, I read in some journals that gravity is basically created when you have something with huge mass. Basically, if you are to stand on a piece of rock thrice bigger than you in space, you will feel an attraction, because the rock has gravity. Many people do not know that celestial bodies actually exert gravity on each other.
As o.m. mentioned, you need a planet sized mass in the center of your ship to create gravity. But you don't actually need a planet sized mass. An asteroid sized mass is more than enough to create gravity. It's not the size that matters, it's the volume of mass itself. Black holes exert a greater gravity than stars of the same size (not that we know exactly how big black holes are) because all its volume of mass collapsed into a singularity making a superdense mass.
All the moons of the planets also create gravity. It may be small, instead of 1g, you get 0.5g or 0.6g, but it's still gravity. How about Mars then?
The answer? Dark matter/god particles whatever you can thing of. If you want to coin a new term such as 'nucleonic' (my term, take it and i'll throw you into a singularity) it's fine too. Your problem will be how to get it to work and how to contain it. You can simply use electical power to activate the matter, and you can simply say that it's placed under the floor. Obviously this is easy to maintain than rotating sections.
Obviously I'm not saying that there is 'dark matter' inside Earth.
Personally, I dislike rotating sections, because even with future technologies the necessity of weekly, even daily maintenance is horrendous. You not only to have to take care of the moving parts, these moving parts are also sections vulnerable to space radiation. Sure, it's a lower level tech, but it's a hassle to maintain.
In one of the episodes of "the outer limits", they show a dark particle that can't be quantified and and looks just like a normal asteroid causing a malfunction in hyperspace drive, trapping two human ships and an alien ship inside the gravity field.