Pretty typical for a dragster to shake in the burnout, Hoosier equipped cars tend to be a bit worse about it as well. It is all about wheelspeed in the burnout being the culprit.
After the release of the button wheelspeed and shock setting play a big roll especially in higher power stuff and dragsters. To soft a shock or to much air pressure can cause a moderately powered dragster to shake the car apart. It also happens in door cars but they are not as susceptible to it as pipe racks are, but the causes are the same.
Here is a video of our dragster on a not so horrible shake session. Stiffen the shocks up a click and knock some air out of it and was all good. Just misread the track a bit. We have had it shake so bad it broke beadlock bolts and bars..This is a moderately powered(1000hp) 4 link car
https://www.youtube.com/watch?v=3Hslwkm9zpsTake out a 1/4lb of air and one stiffer on the shock and viola all new car
https://www.youtube.com/watch?v=tF4QXmXRqU4
