Shaking

Suspension? In the past, have seen bad shock absorber cause a vibration. It only happened at a certain speed. Above or below that speed, no vibration. Just a thought.

Upper strut mounts bad

Don’t know about the thud but the vibration could be bad CV joints in the front axles. Also badly worn out spark plugs can make the engine misfire so badly under acceleration that it creates a vibration.

If u out the tranny in park and step on it and there's no back fire or cut out or esp when u're driving if there's nothing like that it's not the motor,if u here a ticking or worse noise when u turn ure tire it's the CV.joints,shacking when u put on the brake it's ure rotors mise we'll pick up pads to if u're gonna do them it's cheap enough.and if u have vibrating,not jumping, &most of the time a sound it's the wheel bearings most likely, but like me I have a bad jumping when I step on the gas let it go nothing so much so I thought it was the top motor mount bc.s it was snapped but what was jumping around must if snapped it changed it.chanded bearings I kind of new it wasn't that,I blve mb.another motor mont,mb.i was thinking frame mounts but would they go bad enough to make the car jump,thinking CV.joint but it don't make no noise when I turn mise we'll change it thoe.im just hoping it's not where the other side of the CV joint goes into the tranny.if anyone had this problem mb.u could throw me a couple ideas I didn't check every motor mount yet I know stupid but getting outbther and checking td.i hope what I said helped other people with other problems don't ever be afraid to text I'm usally right on but I've been having the kid do some of this stuff and don't know what he checked and didn't.but I'm bringing down for an oil change so I could look under and check if I find the problem I'll tell use.it seems like it happens alot.anothet thing that happens alot on these 2008 grandprixs are the front low beans keep going off in the middle of the night they come on till there burnt out I seen like a hundred complaints about this prob.a sensor idk.should be a recall