Body cavity "tones" in my electric??

I have a HSH Chapman Cap10 - Beautiful guitar but when I am playing it without an amp, it gets these odd tones/vibrations/harmonics that kind of ruin the "acoustic" nature of the guitar. I am baffled as to what to do. Have not heard of putting any sound dampening in the pickup cavities. It makes it not fun to play acoustically. Thoughts or am I hallucinating?