Actually it IS vibrating the floor, just not at the frequencies you would feel.
Acoustics can do strange things. I have a pair of floor speakers in my office that I swear are louder down the hall than in my office.
I used a suspended ceiling in my basement and it did a fantastic job even without adding fiberglass on top of it.
I have used Cork in a similar situation but Torque1st idea of suspended ceiling, especially using the acoustic ceiling would probably be the best bet.
Or find out why it is making the sound.
You may find that changing to larger diameter speakers to eliminate the high notes, or smaller to soften the low notes might just fix it.
I would walk around the living room with the TV running, and see if you are hearing the high's or the lows.
I fixed a not too dissimilar problem at my SIL's place by putting external speakers on her roommate's TV, with small bookshelf speakers near her head while she was listening.
She would have the TV up till the sound was audible in the whole house, as she is a little deaf.
The small speakers much closer to her ears let her enjoy the sound while other people in the house can hear themselves think.
She says she can hear it better, and we couldn't even hear it in the next room.
Did cost a little, but not much. I used PC speakers and the earphone jack, which disabled the internal speakers.
