Lots of us have the shimmy/ shake issue on on Bonneville. Here is the TSB from GM:

Shake/Vibration in Steering Wheel, Floor, Seat at Highway Speeds on Smooth Roads (Diagnose/Balance Tires/Wheels)
1998-2004 Buick Park Avenue, Park Avenue Ultra

2000-2004 Buick LeSabre

1998-2004 Cadillac Seville (SLS, STS)

2000-2004 Cadillac DeVille (DTS only)

2001-2003 Oldsmobile Aurora

2000-2004 Pontiac Bonneville (17" Tires only)

This bulletin is being revised to add the 2004 model year and delete the screened tire program information for all tire manufacturers except for Continental General. Please discard Corporate Bulletin Number 00-03-10-007E (Section 03 - Suspension).

Condition
Some customers may comment on shaking/vibration in the steering wheel, floor or seat while driving at highway speeds (typically between 60-72 mph (96-115 km/h)) on smooth roads.

Cause
These specific vehicles may be sensitive to various rotating mass assemblies, especially if they are considered to be out-of-balance.

Correction
Visually inspect the tires and the wheels. Inspect for evidence of the following conditions and correct as necessary.
Missing balance weights
Bent rim flange
Irregular tire wear
Incomplete bead seating
Tire irregularities
Mud/ice build-up in wheel
Stones in the tire tread
Set the tire pressure to 30 psi (205 kPa) COLD.
Road test the vehicle with the Electronic Vibration Analyzer (EVA) essential tool for a sufficient distance on a known, smooth road surface to duplicate the condition. Record the Hertz (Hz) reading as displayed by the EVA onto the tire data worksheet found at the end of this bulletin. This should be done after a tire break-in period of at least 10 miles (16 km) at 45 mph (72 km/h) or greater, in order to eliminate any possible tire flat-spotting.
If the road test indicates a shake/vibration still exists, check the imbalance of each tire/wheel assembly on a known, calibrated, off-car dynamic balancer. If any assembly calls for more than ¼ ounce on either rim flange, remove all balance weights and rebalance to as close to zero as possible.

Important
Some GM dealers may have a Hunter GSP9700 Road Force Balancer. This will simplify Step 5 by not requiring dial indicators. If a Hunter GSP9700 machine is available, it may also be used to measure the radial force of the tire/wheel assembly. A guideline here is 18 lbs or less.


While on the balancer, measure wheel runout. If radial or lateral runout exceeds .020 in (0.50 mm) for aluminum wheels (.030 in (0.76 mm) for steel wheels), replace the wheel.
After confirming wheel balance and wheel runout, if any changes were made, road test the vehicle again.
If the smooth road shake/vibration still exists:

Important
The completed worksheet must be attached to the hard copy of the repair order.


Record Radial Force Variation readings if you have access to Hunter GSP9700 Wheel Balance equipment. Use the worksheet found at the end of this bulletin to record the readings.
If one or more of the tires have RFV readings in excess of 18 lbs, match mount the tires to get below 18 lbs. Readings of 12 lbs. or less are preferable for critical customer concerns.
If the RFV can not be reduced to an acceptable level, replace the affected tire with one obtained locally.
The screened tire program is no longer in effect for Bridgestone/Firestone, Goodyear and Michelin. Low speed screened tires are available from Continental General only, and only for the Buick LeSabre.
Road test the vehicle to ensure the shake/vibration has been resolved.
Replace both lower control arms on vehicles built prior to the following VIN breakpoints. On Aurora, Bonneville, DeVille, Park Avenue, Park Avenue Ultra and Seville models, a newly developed hydro-bushing lower control arm with improved damping characteristics has been released. This control arm is not used on the LeSabre. The new lower control arms may provide an incremental improvement to the vehicle ride. Customers who have become "tuned in" to the shake condition may still feel some shake in the vehicle after the new lower control arms are installed. Refer to Lower Control Arm Replacement in SI (refer to the Parts Information table below for SI document ID numbers).

Important
THE CONTROL ARMS SHOULD ONLY BE INSTALLED ON VEHICLES IF, AFTER THE TIRE AND WHEEL DIAGNOSIS AND REPAIRS HAVE BEEN PERFORMED, THE VIBRATION CONDITION STILL EXISTS.


Model
VIN

Park Avenue
34175493

Seville (SLS, STS)
3U247643

DeVille (DTS only)
3U247644

Aurora
34175503

Bonneville
34175497


Parts Information
P/N
Description
SI Document

25746324
Lower Control Arm, Left (Aurora, Bonneville, DeVille, Park Avenue, Park Avenue Ultra, Seville)
Aurora -- 639351

Bonneville -- 657809

DeVille w/FE1, FE3 -- 724856

DeVille w/FE7 -- 724858

Park Avenue, Park Avenue Ultra -- 657760

Seville -- 539332

25746325
Lower Control Arm, Right (Aurora, Bonneville, DeVille, Park Avenue, Park Avenue Ultra, Seville)


Parts are currently available from GMSPO.

Warranty Information
For vehicles repaired under warranty, use:

Labor Operation
Description
Labor Time

E0901
High Speed Tire Shake
0.8 hr

Add
Measure Tire/Wheel Asm., Runout and Re-balance
1.3 hrs

Add
Replace Tire and/or Wheel - Each
0.2 hr

E3537
Arm Assembly, Front Control -- Replace
Use Published Labor Operation Time



Screened Tire Request Form (Bulletin 00-03-10-007F)

Fax Instructions:

Continental General : 888-847-3329





Here is the GM document 800385:


Support the brake caliper with heavy mechanic'* wire, or equivalent, whenever it is separated from its mount and the hydraulic flexible brake hose is still connected. Failure to support the caliper in this manner will cause the flexible brake hose to bear the weight of the caliper, which may cause damage to the brake hose and in turn may cause a brake fluid leak.


Remove the brake caliper from the mounting bracket and support the brake caliper (2) with heavy mechanic'* wire (1), or equivalent; do NOT disconnect the hydraulic brake flexible hose from the caliper. Refer to Brake Caliper Replacement - Front .



Remove the brake pads (2) from the brake caliper bracket.
Remove the brake pad retainers (1) from the brake caliper bracket.



Remove the brake caliper bracket. Refer to Brake Caliper Bracket Replacement - Front .
Mount the brake caliper bracket (1) in a vise.
Using a flat bladed tool carefully remove the pin bolt boots (2) from brake caliper bracket (1) and discard.



Remove the bushings (2) by carefully inserting a small screw driver into the brake caliper pin bolt bushing.
Rotate and pull the bushing outward to remove.

Important
Clean all parts in clean, denatured alcohol.
Dry with low pressure, non-lubricated, filtered air.

Inspect the brake caliper bracket for cracks. If cracked, replace bracket.
Installation Procedure





Important
When servicing a brake caliper equipped with the first design caliper hardware it will be replaced with the second design hardware. The second design hardware kit contains NIGLUBE lubricant and redesigned caliper pins. The second design hardware kit does not use bushings in the brake caliper mounting bores.


Using NIGLUBE provided in the hardware kit, lubricate the following:
Lubricate the bores (3)
Lubricate the inside of the pin boots (2)
Lubricate the new caliper pin bolts (4)
Install the new caliper pin boots (2) to the caliper mounting bracket.



Install the brake caliper bracket (3). Refer to Brake Caliper Bracket Replacement - Front .
Install the brake pad retainers (1) to the caliper bracket.
Install the brake pads (2) to the caliper bracket.
Remove the heavy mechanics wire.
Install the brake caliper. Refer to Brake Caliper Replacement - Front .

--------------------------------------------------------------------------------
Document ID# 800385

GOOD INFO HERE,i got the same prob,maybe i should have bought 16'* for my car instead..2003 bonne.

My 04 Bonne SLE has 197k and still has the vibration through several sets of tires, balancing and rebalancing, replaced rotors, etc.
My '11 Impala LTZ has the same symptoms.
Has anyone successfully gotten rid of the vibration? I don't want to waste time or money.

I have heard a lot of great results come from a roadforce balance, not to be confused with the free spin balance most places do.

I had that done once on my Bonne at a GM dealership when it had new RSAs on the front and it made almost no difference. I just got the Impala and am tempted to give it a try.