I would say that if it didn't get worse or better, it was a loose driveshaft. If it were the winter, it could be a chunk of ice stuck in the wheelwell fell onto the tire and was grinding away (scared the bejeesus out of me because in addition to the noise it acted like a brake and made the car pull to one side, I thought I blew a tire).
There is nothing under your seat that should vibrate so the next guess is a loose dogbone mount. This is the engine mount that attaches to the subframe in the middle underneath the car. Another possibility is something related to the clutch. Is there any soot sprayed around the engine bay? All of these should be constant, not coming and going.
Because you said it was exhaust noise, maybe a component related to the EGR blew open? Check for soot spray on the firewall.
There is nothing under your seat that should vibrate so the next guess is a loose dogbone mount. This is the engine mount that attaches to the subframe in the middle underneath the car. Another possibility is something related to the clutch. Is there any soot sprayed around the engine bay? All of these should be constant, not coming and going.
Because you said it was exhaust noise, maybe a component related to the EGR blew open? Check for soot spray on the firewall.