Time-averaged canonical perturbation of nonlinear vibrations of a spinning disk

This paper considers the dynamics of a spinning disk with the inclusion of in-plane inertia. The inclusion of the in-plane inertia couples the in-plane and transverse vibrations of the spinning disk. By considering one mode of each vibration, the problem can be reduced to a non-linear 2 DOF model. An analytical solution of this 2 DOF model is then developed using a time-averaged canonical perturbation approach and is compared with that of a numerical procedure. Through the use of these analytical and numerical tools, it becomes apparent that the inclusion of the in-plane inertia leads to the possibility of internal resonance between the oscillators, depending on the relationship between the natural frequencies of the two oscillators.