Following up on DanH response...

The Free-Free means that neither end of the system is constrained or fixed, and is appropriate to a crankshaft whirling away on one end and the prop on the other end. Fixing some spots along the chain happens when a part is anchored against vibration. A tire tread patch on pavement is pretty good for "fixed".

You have a resonance mode in the operating range at 54 Hz. Looking at the vector, Inertia 1 & 2 are accelerating together while the 3rd and 4th inertia are also accelerating together, but opposite to 1&2. Your prop and engine are vibrating opposite each other with spring 2 (between inertia 2&3) being exercised. This could be a bad thing.

Going to the next mode, that is a firing frequency at 200Hz*40 = 8000 rpm on a three cylinder engine. Firing looks safe unless you are going above 600 rpm, but 4 stroke engines have their second biggest forcing function at 2x firing, so 200Hz also gets pumped by the engine at 4000 rpm which is also inside your operating range. This is pistons going up and down in the cylinders... Now this forcing function at 2x firing tends to be about 1/4 to 1/3 of the amplitude of firing frequency - while smaller, it is usually still important. Springs 2 and 3 are both being exercised, with spring 3 being run much harder. Reading the vector, this mode has Inertia 1, 2 and 4 going the one direction while Inertia 3 is vibrating opposite the other three, and Inertia 4 is amplifying a LOT.

The last one is way up there, probably irrelevant to us. Try out some more inertia in 1 and 2, lower spring rate in 2, and higher spring rate in 3, then see if the last mode has stayed out of range high...

Typical solutions to the 54 Hz mode are:

- Increase inertia 1;
- Increase inertia 2;
- Decrease spring rate 2;
- Combinations of the above.

Typical solutions to the 200 Hz mode are to add stiffness in spring 3 to drive this mode higher.

What parts are these seven pieces? The relative size of the inertia are not really making sense to me. Usually the prop is biggest, engine and flywheel are next smaller, and the sheaves or gear sets are much smaller again... Inertia 1 and 2 are pretty small compared to inertia 4, which I am assuming is a prop, and that is OK, but inertia 3 is bigger than Inertia 1+2, which is unusual. Do you have a flywheel on the engine? Where is it in this scheme?

Then the springs... 2 is softest, but that is still about 2 to 4 times what is used in a typical diesel pickup truck damper spring with about 10 times the torque - not exactly what I would call a soft element in a little engine. The other stiffnesses are only 1-1/2 to 4 times the soft element, which means they are kind of soft.

Usually the soft element is soft while the inertia ahead of it are high to drive first mode below operating and the rest of the elements stiff to run the rest of the modes out of range high. Prop shafts are beefy SOB's as they carry the engine torque times the torque ratio of the gearset in torsion, plus they carry gyroscopic moments from that big prop inertia times prop speed times combined pitch-yaw rotation speed (rotation rates are in radian/s, inertia is in consistent units to get torque units you are designing in). When you make the prop shaft beefy enough to both be reliable under carrying torques and gyro moments and get the higher modes high enough, it tends to be pretty beefy indeed. Usually, you check it out with one set of bearings, and if it is not stiff enough/ strong enough, you go to the next size up of bearings, bump the shaft diameters to follow, through drill it to take out some weight, and check again. When you are done, somebody will try to tell you it is overbuilt. Worry not if it works.

Billski