I have a 2005 Accord. 3.0 v6 237000 miles. I am second owner.
Car had a grinding sound from the front when I bought it so I immediately replaced both front hubs and bearings and did CV axles while I had it apart.
Car had a very violent shake under acceleration starting at around 40MPH If you stayed in it and got it to highway speed the shake went away once you were no longer under the load of acceleration.
So I did the research and decided it needed motor mounts and trans mounts. I was right. Of the six overall mounts on the car, four were broken. Both of the big front and rear dampers were bad, (very bad, the top of the piston was broken out of the rubber completely) the drivers side lower motor mount was completely bad and the rear trans mount had sheared the top mounting plate off.
So I rpelaced them all. Vibration still there only now it comes on at about 55-60 MPH and settles down as soon as you're not under hard accelleration anymore. I also noticed that in the morning when it's cold, the vibration isn't as bad until the car warms up (Maybe the fluid in the damper is thicker in the cold?) I started wondering if the axles I replaced were defective form the factory. (Rock Auto) So yesterday I jacked the car and videoed the axles while the car ran. Granted, it went right into limp mode because the tires weren't making contact but I didn't see any out of round that I could notice. I am baffled. The car runs like a Rolex watch. I can't find the shakes no matter what I do. Seems like it's coming from drivers side.
I was thinking of replacing the axles just in case. They're not terribly expensive. Any suggestions?

 

I don't see if you ruled out the tires. You can try rotating the tires and see if the vibration changes/goes away. I'd also recommend checking the suspension to see if anything is worn out like ball joints. You can try pushing/pulling on the tires at 12/6 then 3/9 o'clock to see if there is any play in the ball joints/tie-rod ends.

 

Tried that already. No change

 

I am baffled. I replaced every ,mount. I rotated the tires. I CANNOT isloate this bad vibration under acceleration at around 55 and up. Car has 237000 miles. Probably needs a set of plugs. Could it be losing a cylinder under load. Highway mileage is not what I expected at 26MPH. If it's misfiring under load, is thaty more likely to be a coil pack? Also, driver's side lower control arm bushing is completely torn. The front where it blots to the frame. There is no rubber / silicone left in that ring. Could THAT be the cause of the wobbles?

 

A loose/broken suspension bushing can cause your problem. I'm guessing the compliance bushing is shot. The bushings can be replaced. The hard part is the bolts can be frozen in place to remove the lower control arm. I ran into this and ended up replacing the control arms vs replacing the bushings. My car lived in the northern us and the salt made removal very difficult, where I used a Sawzall to cut out the bolts. I also broke off one of the welded nuts on the subframe and replaced the subframe with junkyard part.

 

I'm replacing the whole thing. I don't think it's worth trying to just replace the bushing

 

Did the shaking happened worse after you replaced axles?? I've seen bad axles cause the same issue

 

Yes. I noticed it right after changing the axles