Not sure if it is a vibration "motor" per se rather it may well be a solenoid. A solenoid works on the principle of electromagnetism moving a demagnetised ferrous armature up and down within a stem tube, surrounded by copper coil acting as the "magnet". If the wires connecting to the solenoid are suffering from a "dry solder joint" or "fractures" or quite simply "poor connection" then it is easily remedied through another carefully applied drop or two of solder.

When soldering be careful not to short across any of the other lands (conneciton points on the board) for fear of permenently and completely bricking your phone.

From the short description of shaking it I would guess at a dry solder joint in that area. Although not sure where it would be......

Hope this helps....