Free torsional vibrations of an elastically connected double-shaft system

In this article, a theoretical undamped torsional vibration analysis of an elastically connected double-shaft system is presented. The double-shaft system is one of the simplest model of a complex continuous system, which is composed of two concentric, cylindrical circular elastic shafts attached together by a Winkler elastic layer. The free transverse vibration problem of this system is considered by using the separation of variables method. The boundary value and initial-value problems are solved. The natural frequencies and natural mode shapes of vibration are determined. The free vibrations of an elastically connected double-shaft system are realized by synchronous and asynchronous angular displacements.