Steady-state and transient responses of a flexible eccentric spinning shaft

Abstract

The steady-state and transient dynamics of a flexible spinning shaft with eccentricity driven by a DC motor (i.e., non-ideal energy-source) with external and internal damping is studied in this paper. It is well established that the structural response of a vibratory system to which a non-ideal drive is connected may act as an energy sink under certain conditions such that a part of the energy supplied by the source is spent to vibrate the structure rather than to increase the drive speed. This phenomenon is formally known as the Sommerfeld effect. The Sommerfeld effect characterized by jump phenomena is studied through the steady state amplitude obtained by instantaneous power balance method and further verified through numerical simulation. Transient responses of non-dimensional amplitude and shaft speed with time evolution through first mode resonance are also given.

Keywords

• sommerfeld effect
• non-ideal source
• internal damping
• instantaneous power balance
• transient response
• spinning shaft