Normally if the shimmy occurs at around 50-60 mph, I would suspect a tire out of balance. However if the shimmy is constant, it may be a bent wheel, loose wheel, loose wheel bearing, or worn suspension parts. Have your tires rotated and balanced. At that time have them check for a bent wheel. Make sure when they install the wheels back on the car they are torqued to factory specs. Have them inspect your front suspension parts for damaged or worn parts. Can also be a defective tire. Look for bulges on the sidewall, or a tire that is wearing unevenly. Make sure the tires are aired up to the specifications listed on the driver's door post or in your owner's manual. No more no less.
The 2011 Jeep Grand-Cherokee has 58.6 in. of front shoulder room.
The 2004 Jeep Grand-Cherokee has 39.7 in. of front head room.
The 2004 Jeep Grand-Cherokee has 56.5 in. of front hip room.
The 2004 Jeep Grand-Cherokee has 41.7 in. of front leg room.
The 2012 Jeep Grand-Cherokee has 40.3 in. of front leg room.
This is a self-exited vibration problem.
The 2009 Jeep Grand-Cherokee has 59.1 in. of front shoulder room.
The 2002 Jeep Grand-Cherokee has 56.5 in. of front hip room.
The 2011 Jeep Grand-Cherokee has 58.6 in. of front shoulder room.
The 2012 Jeep Grand-Cherokee has 39.9 in. of front head room.
The 2013 Jeep Grand-Cherokee has 57.0 in. of front hip room.
The 2004 Jeep Grand-Cherokee has 39.7 in. of front head room.
The 2007 Jeep Grand-Cherokee has 57.1 in. of front hip room.
The 2013 Jeep Grand-Cherokee has 39.9 in. of front head room.
The 2009 Jeep Grand-Cherokee has 41.7 in. of front leg room.
The 2011 Jeep Grand-Cherokee has 57.0 in. of front hip room.
The 2010 Jeep Grand-Cherokee has 57.6 in. of front hip room.