The aircraft will normally shake a bit on take-off as well with often the cabin fittings making quite a lot of noise (and again this does seem to get worse as planes get older).
Some particular types have distinctive noises and vibrations as well...the HS 146's flaps being one well known example. The A320 if remember rightly sometimes makes a noise that sounds rather like an electric drill. Most turboprops give off a distinctive 'beating' sound from the propellers on take off which is caused by the revolution speed not quite remaining synchronised as the plane accelerates. So there are lots of noises and shakes...most of which are completely normal.
One which I couldn't identify once was on take-off in the 777...just prior to and after lift off there seemed to be a lot of vibration coming from the undercarriage...I thought that perhaps there was a rough patch on the runway at Gatwick...does anyone have any idea?