The failure to see or understand something does not mean it does not exist. It means that you will be surprised.

While an exact understanding of all the vibration characteristics is beyond our current ability, it is possible to get a first order approximation through careful measurement and testing. Late last century I designed a propeller for my Lycoming powered L-IV. I fabricated the blades from 4" 2024 aluminum plate on a CNC milling machine I also built. I used a Hartzel hub and machined an adapter for the Lycoming. Once I put all the pieces together I took the propeller assembly to Sandy Friezner at Specialized Testing Service where we connected it to an electrodynamic shaker. We then shook the propeller through a range of frequencies to determine the resonant modes. Sandy already had the data for the Lycoming and was able to identify 2,200 RPM as a match between engine vibrations generated and frequencies that would "excite" the propeller. The conclusion was that the engine should not be operated continuously at 2,200 RPM as a fatigue failure of the propeller at this speed was possible. Let the test flying begin!

Certified propellers are designed and tested so that their resonate frequencies fall above the anticipated range of frequencies produced by the engine. Increase the number of cylinders from 6 to 8 and you increase the frequency of some of the vibrations by 33%. Increase the engine RPM (gear box) and you push the frequencies even higher. It is not just possible but likely that by putting a propeller certified for a direct drive 6 cylinder or turbine on a geared 8 cylinder you will have the ability to excite a vibration mode of the propeller at an RPM within the operational range.

The 50 hour test flight time is not random. It gets you to about 10 million vibration cycles which gets you past the knee in the fatigue limit curve FOR STEEL. If you make it past 10^7 cycles you likely make it to 10^9 cycles (5,000 hours). However, Aluminum has no such knee. This is why there are airplanes that have run out of "life" sitting in bone yards.

On the topic of gears, while it is true the helical gears have higher tooth engagement fractions they also have some disadvantages. They produce significant thrust loads on the gearbox housing (sine of the contact angle times the tangent contact force) which require additional mass in the bearings and housing to deal with the forces. Also they are significantly less efficient. Spur gear efficiency rule of thumb is 1% loss per interface. Helical gears, because of the sliding action, are about twice that so if you are transmitting 800 horsepower you are putting 6,000 watts of heat into the spur gear but more than 12,000 watts into the helical gear. For an idea of scale, the primary radiator is dissipating about 120,000 watts.

I believe the Bugatti Veyron, which produces a nominal 1,000 horsepower, has 10 radiators to deal with the heat. The Veyron has a top speed of ~220 Kts.

The Rotary engine does have some advantages for aircraft application. Lacking a connecting rod, the primary vibration is a pure sinusoid and the one power pulse per revolution per rotor gives a 4 rotor the same torque ripple as a 8 cylinder piston engine. The "yes but" of the Wankel design is the really bad combustion chamber shape that leads to high fuel consumption. Also, having a 10:1 effective compression ratio limit prevents implementing a direct injection compression ignition (diesel) cycle. Curtis Wright spent years and millions developing their SCORE (Stratified Charge Omnivorous Rotary Engine) family of Wankel engines but ultimately sold the design to John Deere.

After more than 100 years, the prime mover of choice still has a piston, rod and crank. There may be a reason for that.

Regards
Brent Regan