I've had this problem since 6 months after purchasing my 99 SE V6 5sp new. Pretty much guaranteed to happen any time there is a fair amount of water on the road (I live in Seattle so this is fairly often). Typically occurs during highway driving and it's a very loud grumbling -- sounds like a hole in the exhaust header-- with vibrations between 2000 and 4000 RPM.
The vibrations are more like someone hitting the under carriage with a hammer as opposed to just a vibration, in my situation. It's a bang bang bang which increases with RPM. If this was rear wheel drive I'd swear part of the driveshaft was banging against the bottom of the car, or that there was a guy stuck under there with a ballpeen hammer trying to escape. Notably if I put the car in neutral and run thru the RPMs the pounding is less if not non existant but once back in gear it's hammer time again.
This occurs with the AC on, AC off, defroster on, defroster off, day, night, headlights on/off, fog lights on/off, even turned carr off and back on while rolling down the highway to see if it would go away once restarted -- I've been trying to diagnose this for almost six years now....I've checked almost every scenario possible.... I think

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Typically the vibration and knocking will occur for about 30 seconds then stops. Sometimes it occurs again within a few minutes, sometimes not for a few days. But only when it is pretty darn wet.
I've talked to the dealer on multiple occasions, they never find anything. I was surprised because the pounding is so forcefull I would have expected some form of marks or dents under the drivers seat.
In any case this is a problem which several of us posted about back in 99 with the orginal camryguy/solara guy website. Glad to see that it is still an issue and that I'm not just a crazy insane guy. Plus I can print the posts out and take it to the dealer to show that I'm not the only one with this mystery issue.