Rumbling ?

You need to better isolate the table. It sounds like you are getting a little low frequency feedback. This is why some preamps had a filter to roll off the bass below 20hz.
I've also found you could lower the dustcover down while playing and this will stop it sometimes.

Dear Pboutin: Which TT/tonearm/cartridge do you use? and what level/volume happen that? with all kind of music/with all LPs ?

Please give us some info about .

Regards and enjoy the music.
Raul.

You may want to do a simple test to see if Bigtee's suggestion, and it is a good one at that, that acoustic feedback may be the issue. Lower the stylus into the groove with the motor off and the platter NOT spinning. Advance the volume a little bit above your normal listening level and lightly tap the shelf that the table sits on. If the rumbling starts, it will rapidly increase in level. This is acoustic feedback. Turn the volume down immediately. You will need to better isolate the turntable. Check the archives here, there are many possible solutions.