There have been various posts detailing a vibration or wobble on this generation Camry through a particular speed range. In my case it has been between 45-55 MPH when accelerating. Many of us have had the tires changed, balanced, rebalanced, wheels checked for roundness, suspension parts changed, axles replaced, etc.
This problem first started for me 3-4 years ago and no mechanic has been able to pinpoint the cause. Finally a stroke of luck has befallen me and I have discovered the problem and fixed it. In my car the problem has been the motor mounts. I replaced the one by the radiator when the engine was rocking back and forth when first starting out. After replacing it I noticed the dogbone mount was dried out also. That one was easy to replace.
Since replacements of the mounts, the wobbling sensation has mostly ceased. If there is any at all, it is around 30 MPH. Perhaps the third mount is worn or something else, but at this point I am ecstatic. Let me tell you, it's like driving a new car again. There also seems to be more power available. Perhaps that's just my imagination, though. The total cost to repair the two problems was $110. $70 for the big mount from Advance Auto and $40 for the dogbone from NAPA. A pneumatic impact wrench and breaker bar is also neccessary.