Park Avenue shakes when accelarating between 30-40 mph.

Park avenue 2001, 3.8V6. 96000 ml.
It runs very well until recently, it started to shake between 30-40 mph when I push the pedal.

typically, when I push the accelerating pedal steadily from 0, it will smoothly go up to over 50mph with slightly pausing when it change gears. But when the speed is between 30-40mph, if I release the pedal, then when I push it again, I notice the shaking. It feels like the car is pausing very quickly. The speed will not go up. Release the accelerating pedal, shaking stopped. If I push the pedal slowly, it will not shake and the speed goes up.

what kind of problem it can be? Misfire? Bad torque converter? A bad clutch?

Btw, No warning light on the panel.