Super-harmonics in a torsional system with dry friction path subject to harmonic excitation under a mean torque

The nonlinear frequency response characteristics of a two-degree-of-freedom torsional system with a significant dry friction controlled path are studied, when excited by sinusoidal torque under a mean load. An analytical solution is first developed for a simplified system subjected to continuous slipping motions. The nature of super-harmonic peaks as generated by the dry friction nonlinearity is efficiently found. The effect of a non-zero mean load is also determined and qualitatively understood. Further, a refined multi-term harmonic balance method (MHBM) is proposed that includes up to 12 terms. It is used to study an automotive drive train system that experiences significant stick–slip motions. Associated computational issues including the selection of initial conditions are addressed. Studies show that the mean load could induce asymmetric stick–slip motions and accordingly it has significant effect on time and frequency domain responses. Reasons for the occurrence of super-harmonic resonant peaks and transitional peaks are investigated. Finally, our MHBM is applied to the conventional single-degree-of-freedom system where the spring path exists in parallel with a dry friction damper (Den Hartogʹs problem). Our predictions match well with Den Hartogʹs analytical solution. Den Hartogʹs system differs, in terms of the dynamic behavior, from our torsional system (with a sole dry friction path).