Add an option. Guy's , sorry that I didn't do this a bit better.
Bernie, I think that a combination of a somewhat aggressive rake & trail configuration that gives the fjr it's nimble feel but makes it susceptible to the shakes and I also believe the use of ball bearings in the steering head contributes as well, the gl1800 suffers as well from this, the ball bearings are meant to provide an easier, smoother steering action whereas the tapered bearings because of the much larger contact surface area adds drag/dampening plus the ball bearings are cheaper to buy at the oe level which even if it's only a penny cheaper each, over a total production run provides a big cost savings.
Looking at the results so far it appears that it's a way more prevalent problem than Yamaha will admit..
Steve, your mention of rake making the FJR susceptible to the shakes is true, and this made me think of what I had done to my bikes. I have always thought that the front suspension on the FJR's, as set up to factory specs, had the springs too soft and the compression damping too hard. So, the first thing I did to all my bikes, is screw the spring preload to maximum hard, and reduce the compression damping by 4 clicks.
Soft springs = too much sag = reduced rake = less stability.
increased preload = less sag = increased rake = more stability.
Also, I am a fairly small guy, weighing approximately 190 pounds wearing full riding gear, which again means less sag than a heavy guy would cause, which means more stability as explained above. I wonder if the combination of a very heavy rider combined with too much sag in the front suspension, is enough to tip the bike from stability to instability and head shake????
As an aside, I have known for years that, having a heavy pillion passenger on the bike increases stability because the pillion's weight causes the back of the bike to squat, which increases rake, increasing stability.
Acceleration does the same thing, the back end squats, and stability improves, whereas deceleration and/or braking causes front end dive, less rake, and instability.
Head shakes and tank slappers nearly always occur when the bike is decelerating and/or during braking. So, perhaps the solution to this problem is to increase your front preload, or fit stronger springs, and go on a personal diet.