I agree with DmaxMaverick look for a loose steering box first and also look for a cracked frame at or near the steering box bolts. Additionally, check for out of round or badly out of balance tires. If you still have the shaking issue you should consider buying a steering dampening shock kit.
With the tires on the ground have someone turn the steering wheel while you look at the steering box from above. If the frame is cracked it will be very easy to see. Yesterday I welder the frame on my neighbor's 85 Suburban and installed a reinforcing kit that he purchased at a off road shop. Loose steering boxes and cracked frames are a common problem especially if you added large tires and wheels. Let us know what you find.
Good luck
John
*2006 Chevy, 3500, 4X4, DRW, (LBZ) D/A, CC, LT, 252K Miles, 19.5" Wheels, Mag Hytec Transmission Pan and Differential Cover, SS Grill Guard, Racor 2 micron aux fuel filter, 100 Gallon Aux Fuel Tank, using Edge Evolution, Predator Diablosport, Kennedy ECM tune, Fitch Fuel Catalyst.
*2006 Four Winds, Dutchman, 36', RV, D/A, 5500 Kodiak.
*1993 Harley Davidson, Turbo charged, Springer Softail.
*2007 Pontiac Solstice.
*2005 Jeep, Liberty, CRD (diesel).
*Full-timing in USA, see America first.
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