I am having an issue with my car shaking when I apply the breaks. At first, it would shake horribly if I was driving over 30 mph or so. I thought it was the front rotors and replaced them twice but it didn’t help.
Eventually I took it to be looked at. The tie rods were in bad shape. I had the tie rods replaced and had an all wheel alignment.
Now the cars drives much better and does not shake near as bad as it did before. However it does still do it on an intermittent basis. Now it feels like the vibration is more in the brake pedal/steering wheel rather than the body of the car.
If your car is breaking, that should explain the vibrations quite nicely, although after a couple seconds (when you hit the pavement,) the vibration would be the least of your concerns.
My understanding is that the warped wheel hubs can result from the tie rod issues you had previously.
My somewhat paranoid but hopefully effective advice: If you have a secondary trusted mechanic (e.g. if you took the car in for the tie rods at a local shop, try a chain, or vice versa) have the car checked out and don’t mention anything about the previous work until after they give you an estimate or get back to you on what they think might be wrong. I would bet that Gary T’s ideas are spot on, but you can’t know for sure until you have the car checked out again.