A pair of shafts, connected by gears, forms a mechanical system having a number of modes of vibration. Each mode involves a combination of torsion and flexure of the shafts and of bending of the meshing gear teeth. A method of finding these modes, together with their corresponding natural frequencies, is described and illustrated by a numerical example. Such modes can be set into resonance by, amongst other things, the oscillating forces which arise in the tooth meshing process.
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