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How do I eliminate vibration?
From a practical standpoint, you cannot eliminate all vibration within acceptable weight limits but you can do a lot to mitigate it.
The first step is to balance the engine and prop to eliminate the shaking caused by being out of balance in the first place. The engines on private jets are routinely balanced to less than 10% of their normal balance specification to reduce vibration and hence, noise.
For treatment, isolate the vibration away from the structure.
Since the engine is the biggest generator of vibration, this means installing the correct engine mounts designed for your style of flying and changing them every few years since they do age and loose effectiveness.
Sorry, we cannot help you with these things but you can have this done at most engine shops.
The goal of isolation is to have the shaking mass of the engine vibrate out of phase with the airframe with the energy dissipated as low grade heat in the elastic mount.
