Jim in NC writes:
I think you will find that they do it on ships, with pure weight. A
big,
heavy, solid steel shaft. Very heavy! That is how they get the
stiffness.

Sheesh. Shaft weight is not a factor. And more stiffness may or
may not be desired.

Shaft stiffness is one of the parameters that may be adjusted (up OR
down) so that the system has a natural frequency not matched by a
significant exciting frequency. If the system is driven by internal
combustion, identifying the most significant exciting frequency is dead
simple. It is (RPM x #cyls)/120 = hertz for a 4-stroke and (RPM x
#cyls)/60 = hertz for a two stroke. Designing a system with a natural
frequency that does not match the exciting frequency identified by this
equation is easy IF the engine runs at one RPM only. It gets a lot
harder if you expect to use a wide RPM range.

Also, the shaft turns very slowly, so there are many pulses per
revolution;
more than you will get with a 4 or 6 cylinder, 4 cycle airplane engine,
in
most cases.

Sheesh again. Shaft rotational speed alone is not a factor.

Shaft speed AND number of propeller blades may be of interest if
disturbed flow is the source of an exciting frequency. "Pulses per
revolution" sort of defines the term ''order" as it is used in
rotordynamics (the number of times anything happens per revolution). A
handy term, nothing more. For example, a ship's shaft at 90 RPM turns
1.5 times per second. If it has a four-blade prop and a single source
of disturbed flow (perhaps a strut supporting the shaft), then the
disturbance is a 4th order event. Order times rotational speed per
second (4 x 1.5) means an exciting frequency of 6 hertz. In this case
let us hope the engineer designed a system with no natural frequencies
between 4 and 8 hertz.

Wnat another example of speed x order? Consider the cardan joint.

I agree with the rest of your post; dig into the engineering text
books.

I wish you well with them.

Dan