Dynamics of a non-ideally driven oscillating system under frictional slip

Abstract

The Sommerfeld Effect pertains to the non-linear jump phenomenon near the resonance frequency of an excited structure powered by a non-ideal drive that is incapable to supply the required power to the oscillating sub-system. Often this situation is dealt with by increasing the viscous damping present in the system at the expense of considerable power loss. However, the use of non-viscous damping for the attenuation of the Sommerfeld Effect is considered in very few articles. In this paper, the dynamics of a non-ideal DC motor-driven vibrating system with frictional slip as the dissipation element is presented. Use of the method of multiple time scales is employed to find the response of the system semi-analytically. The non-linear dynamical characteristics of the response as the motor speed crosses the resonance condition is analyzed using the linear stability analysis and subsequently, the obtained response is verified using numerical results. The transition of the operating condition between stable and unstable zones and the post-resonance dynamic behavior of such systems indicated that under proper parametric condition, it is possible to achieve a smooth variation of operating speed via a combination of stick and slip motion. Furthermore, the rate of voltage increment is also found to play a pivotal role in surpassing the critical speed of the system.