Hello and welcome to Just answer,
The noise you hear and feel is the upper intermediate steering shaft, there is a GM bulletin on your concern, when the bulletin was first issued in 2002 the fix was to remove the shaft and lube, this would fix the concern but it would come back, since then GM has revised the bulletin, the new fix which is a permenant is to replace the shaft.
This shaft is the shaft that connects the steering column shaft to the steering gear.
If you attempt the repair yourself do not allow the steering wheel to turn with the shaft removed or the air bag components could be damaged.
Below is a copy of the bulletin.
#00-02-35-003N: Clunking Noise Under Hood and Can Be Felt in Steering Wheel and/or Steering Column (Replace Upper Intermediate Steering Shaft (I-Shaft) Assembly) - (Mar 26, 2008)
This bulletin is being revised to add diagnostic information (refer to Diagnostic Tips) to check the lower steering column bearing as a potential source of the noise. Please discard Corporate Bulletin Number 00-02-35-003M (Section 02 -- Steering).
Some customers may comment on a clunk-type noise coming from under the hood that also can be felt in the steering wheel. These conditions may be more noticeable when turning at low speeds on rough road surfaces.
Use the information below to help diagnose the source of the noise.
DON'T DO THIS
Replace the I-Shaft with P/N 19153614.
Do NOT lubricate or exercise the I-Shaft.
Replace the steering column upper intermediate shaft with an improved design shaft that will eliminate the clunk noise using the procedure listed below.
Notice: On the 2002 and later model year vehicles, the steering column LOCK was removed from the steering column. It is critical that the J 42640 - Steering column Anti-Rotation Pin is used when servicing steering columns on 2002 and later model year vehicles. Failure to use the J 42640 may result in damage to the SIR coil.
Tighten Tighten the bolt to 47 N·m (35 lb ft).
Tighten Tighten the bolt to 50 N·m (37 lb ft).
Tighten Tighten the nuts to 20 N·m (15 lb ft).
Shaft - Upper Intermediate Steering