Complex Dynamics in the Quadratically Non-Linear Response of a Rotating Ring With Elastic Hub

✍ Scribed by R.I. Zadoks; C.M. Krousgrill Jr.

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 694 KB
• Volume: 165
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1993.1266

✦ Synopsis

The truncated quadratically non-linear partial differential equations of motion of a rotating ring with an elastic hub subject to temporally harmonic point loading are derived using Hamilton's principle. The system is reduced to a set of two second order ordinary differential equations by using a single (axisymmetric) mode to approximate the spatial distribution of the lineal displacements. Periodic solutions of the discretized equations of motion are constructed using a shooting technique. The bifurcation behavior of the response is investigated by varying both the amplitude and the frequency of the forcing. This behavior includes the phenomena of turning point bifurcations and period-doubling cascades, the latter leading to chaos.