Although non-linear systems subject to combined parametric and external excitations have been examined in some depth, very few of these investigations have addressed the influence of a mean (time-invariant) load on the system response. In particular, the importance of the mean load effect has been highlighted in the study of whirling asymmetric shafts, where significant changes in system response and stability occur under the influence of gravity. The present paper intends to characterize the specific effect of mean load on the dynamic behavior of a single degree-of-freedom Hill’s oscillator with a clearance type non-linearity while also being subjected to a periodic base displacement excitation. The parametric continuation technique and method of harmonic balance are used for this purpose. Issues discussed include the coupling between the mean load and the dynamic response amplitude, interaction between the parametric excitation effect and the clearance non-linearity and comparison between time-invariant and time-varying systems.

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