On the existence of chaotic circumferential waves in spinning disks

We use a third-order perturbation theory and Melnikov's method to prove the existence of chaos in spinning circular disks subject to a lateral point load. We show that the emergence of transverse homoclinic and heteroclinic points respectively lead to a random reversal in the traveling direction of circumferential waves and a random phase shift of magnitude $\pi$ for both forward and backward wave components. These long-term phenomena occur in imperfect low-speed disks sufficiently far from fundamental resonances.