My dragons have a... "difficult" personality.

They're very catlike. Sure, they're more like KrimsonRogue's cat (somewhere around chaotic good). But, if I want to make my dragons smug, blue-blood a-holes that you still want to cuddle, then I might as well give them the ability to purr very loudly.

Well, that actually would have one tangible advantage, if the dragon could use it to transmit data and instructions to the nanomachines in their body.

Problem is, dragons here are about as large as a draft horse, are filled with spongy and hollow structures on top of having air sacs to assist breathing, and I'm afraid that would ruin the acoustics.

There's also that large cats (lions, tigers, etc...) can't purr.

So, how would dragons be able to purr very loudly?