That shake in a traction elevator going down often means the guide shoes are worn or rails are loose. Check the car sling bolts for tightness, since vibration loosens them over time. Also, the motor brake might catch unevenly during descent, causing a jerk. Have a technician look at the sheave and rope tensions to rule out imbalance.
Interesting take from @jakeadams, but from my experience that shake on descent usually points to rail alignment issues before guide shoe wear. I've found the leveling device can also cause a jerking feel if it's starting to act up.