Recently I noticed a "thunking" noise when I accelerated from a stop and a vibration between 50 and 60 MPH. For what it is worth, I baby this vehicle. I took it to the shop and had three U-joints replaced, the next day I noticed a severe vibration was still there. I returned to the shop where they kept it for two days and cannot figure out what is causing the problem. They re-balanced the tires, checked the alignment, brakes, calipers, rotors and even had the drive shaft re-balanced (which they said was out by 30,000) and took it to a local transmission shop who said the problem is not in the transmission but it is still occurring. They finally admitted defeat and suggested I take it to the dealer. It has 149+ thousand miles on it and a 5.4 engine. I don't want to get into a sob story here but money is tight for us retired guys who don't know squat about vehicles.

So before I drag it to a dealer I thought I would turn to the experts for some help, hints whatever. Any help would be greatly appreciated.

 

Most of the time this relates to wheels/tires. I have had what they used to call 'freeway hop' on many vehicles over 50 years, from every cause there is. The hardest one to solve was a Jeep Cherokee. I did everything, or so I thought, to no avail, including balance, alignment, check wheels for true, wheel bearings, steering stabilizer, etc. I finally decided to sell it but had to put new tires on it because the old ones were shot. Presto-chango, new car. Like riding on a cloud. It was so great I kept it for a few more years, and I wish I still had it, but I digress.
So what the heck was the problem? I'll cut to the chase; my oil change joint had been over-inflating my tires for years. I mean 45-50 PSI instead of 32, and I was not checking behind them. This is very destructive to regular car tires or light truck tires and results in belt separations which make the tires 'lumpy'. That's where the vibration was coming from, and it was also wrecking my front brake rotors by causing the rotor to hit the brake pad at the same spot every revolution. So I would turn the rotors and the brake chatter would come back. After getting the tires I put new rotors on too. The car was great after that until I sold it to an idiot who put 'rims' on it and a big stereo, after which it promptly got stolen and stripped.
So. Visually check your tires for belt separations or have them checked. And to everyone, always check tire pressures after anybody touches your car for any reason. Set pressures cold and leave them alone (don't let air out after the tires warm up) and never put in more pressure (cold) than called for on the door/body sticker.
If your tires are old anyway, don't put it off - get new tires. Check the wheels for runout (should be done when they are balanced but ask for it). Old tires have killed many people from hydroplaning. You know when they should be replaced - just do it.