Thank you all for your really insightful comments!  I tried a few more
things, including some your suggestions -- made sure the wheels were
aligned, checked tire pressure, etc.

I noticed that the problem was much worse when I was on smooth
asphalt, but would almost disappear when I was riding on gravel,
cobblestones, or bricked sidewalk, so it occurred to me that the
problem was this "harmonic" vibration -- not that the bike was out of
alignment, but that it was too perfectly aligned.  So on a whim, I
*loosened* the bolts to the rack -- not enough that the rack wobbles
or is in danger of coming unscrewed, but just enough that there can be
some miniscule "give" between the rack and the frame.  My idea was
that if I could disrupt the perfect transmission of this vibration,
then it wouldn't radiate to the front wheel, but would cancel itself
out.

It was the exact opposite of DougP's suggestion and the opposite of my
original inclination, but it worked!  It went from violent shimmy to
completely smooth.  No shaking at any speed.

Is this perhaps another version of the "self-restoring force" Ken was
talking about?  (The maths are also beyond me.)  In any case, if the
problem happens again in another context, I'll be sure to look into
"tire damping" (nice term) as a first resort!

--

Thanks again, everyone! I'll finally be posting pictures of my AHH
soon, now that I've got it properly scratched up and broken in.  Five
months in Berlin, and besides the daily commute, a few wonderful day
rides already, and and now some inn-to-inn rides planned for fall.

Nicole


P.S. in answer to Ken's question -- neither me nor my mechanic are
well-skilled.

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