Gordon Arnaut wrote:
Another contributor of excitation is imbalance in a rotating or
reciprocating mass.

True, but it has limited power compared to gas pressure
oscillation. I was trying to keep things simple.

Yet another source of excitation in airplanes is the spring effect of
the prop

Naaaa. Propellers in disturbed flow can excite the system, but
usually the concern is the opposite. Might be a few rare causes. For
example, I've seen (with telemetry) a variation in torsional vibration
due to a propeller-powerplant whirl mode.

a crankshaft has its own natural resonant frequency and will vibrate
if it is disturbed with enough force.

Actually a crank has N-1 natural frequencies, where N equals # of
inertias. That would be four frequencies for a typical 4 cyl with 90
degree throws (4 crankthrows plus flywheel, 5 minus 1). However, to be
fair, when designing a PSRU you can model the crank and flywheel
assembly as a single mass moment of inertia, IF the crank is short and
stiff. The inaccuracy in F1 prediction will be small, like 200-300
RPM.

A flywheel is a simple example of a damping device. It uses
centrifugal force to counteract and overcome the twisting.....

A flywheel is an inertia. A damper is a device that removes energy
from the system, usually as heat. Think slipping clutch, slipping
v-belt, or viscous ring damper. Designed a viscous disk damper and ran
it parallel with a soft element in a drive a few projects back. It
shed a lot of heat, and telemetry said it damped resonant amplitudes
very well. The successful Raven drive for the 3 and 4 cyl Suzukis uses
a dry frictional damper.

Ahhhh, I'll let you correct the part about centrifugal force g

This shows that mass is important, unlike some erroneous comments
that mass doesn't matter.

Who said anything about mass? For the record, please note that the
previous comment was "Shaft weight is not a factor", the context being
ship propulsion. Shoot, I'm all for careful use of terms. In the
context of torsional vibration, what IS important is "mass moment of
inertia". And that ain't the same as mass or weight.

Ok, you argue that torsional problems can be eliminated through the
use of flywheel mass and stiff shafting. I argue that your approach
has severe drawbacks when applied to the subject at hand, a long shaft
aircraft system.

I agree that a large-inertia flywheel (which is not necessarily a
large-mass flywheel) always reduces vibratory amplitude. It may not
be reasonable to incorporate a huge flywheel inertia in an airplane
because of effect on (1) handling (remember the Sopwith Camel), as well
as (2) aircraft empty weight. You must use a moderate flywheel, a
compromise, not the infinite inertia you describe.

As for stiffness in the shafting that connects the inertias, what
magic did you have in mind? All practical shaft materials exhibit a
stress-strain relationship. I know of only one practical PSRU concept
that meets your goal of near infinite stiffness; it has no shafts at
all other than the crankshaft. Hardly the long shaft system under
consideration. With a shaft several feet long, some degree of twist is
physical reality.

Given that infinite stiffness is impossible in the long shaft
system, I'll tell you what you'll really get. A stiff shaft will raise
the system F1 so that it intersects the gas pressure oscillation order
somewhere up in the operating range close to peak torque. The system
will resonate into junk. The classic solution then tried by the
uninformed is to make it "stronger" (the result being stiffer), which
makes the problem worse. Near idle or below idle is where you want the
intersection of F1 and gas pressure frequency, because gas pressure
oscillation isn't very powerful at idle. You do that with a soft shaft
or rubber element, and note that it doesn't take a huge inertia to
smooth a small near-idle-speed oscillation. By tailoring frequencies,
we can get a practical, lightweight system.

Nobody can teach this subject in RAH posts. Hell, "Practical
Solution" is several volumes. What we can do is (1) direct folks to
quality reference material, and (2) quit telling them it is impossible.
I think I'll puke if I see one more guy reference the Hessenaur
article and declare "torsional vibration even beat Rutan". If somebody
had handed Burt the right books or introduced him to J.P. Den Hartog,
you can bet you wouldn't be reading that crap.

Dan