Ted asks:
<< Is there an instrument that can be attached to the engine somewhere that will measure frequencies to assess likely nodes of "don't run there?"
>>

The short answer is no.

Imagine a rod with an accelerometer mounted half way down its length. Excite the rod at its second harmonic and the accelerometer  will see no acceleration or displacement as it is sitting on a "node". If the rod were 360mm long the nodes are at 0mm, 180mm and 360mm with the points of maximum displacement and acceleration at 90mm and 270mm. These will also be the points of maximum stress, unless the ends or the rods are fixed, then the maximum stress will be at the ends.

Someone experienced in these matters and with a detailed knowledge of the engine system would be able to put some accelerometers on the engine at various locations and use a spectrum analyzer to determine the vibrational energy distribution versus frequency and then connect a shaker to the engine and see what "buzzes", but this is a lot closer to art than science.

In response to my comment <<< After more than 100 years, the prime mover of choice still has a piston, rod and crank. There may be a reason for that.>>>

William observes: <<< The piston engine was invented first.>>>

True, but the Wankel engine first ran February 1, 1957,  54 years ago. Actually, to be accurate, Wankel's pure rotary design DKM 54 (Rotor and housing rotated) ran on that day. Froede's epicyclic configuration, the KKM 125, what we now recognize as the Wankel engine, first ran on July1, 1958.

If the Wankel engine is superior it has had plenty of time and opportunity to prove it. I have a collection of rotary engines including ones for model aircraft, powered hang gliders, snow mobiles, lawn mowers and race cars demonstrating that the Wankel has been exposed to all these markets yet has failed to dominate any of them.

In the last 50 years entire industries based on new technology have come and gone. While I love the round motor it is hard to reconcile the claim of rotary superiority in an environment where significantly better technology quickly conquers the market.

The Wankel may be the better engine, just not better enough.

Regards
Brent Regan