Analysis of periodically forced nonlinear Hill's oscillator with application to a geared system

Although nonlinear 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 Hill's oscillator with a clearance-type nonlinearity while also being subjected to a periodic base displacement excitation. The parametric continuation technique and method of harmonic balance would be used for this purpose. Issues discussed would include the coupling between the mean load and the dynamic response amplitude, interaction between the parametric excitation effect and the clearance nonlinearity, and comparison between time-invariant and time-varying systems. Further, a geared system has been analyzed as a practical application of the nonlinear Hill's equation examined. Earlier studies on gear dynamics have been reexamined to provide improved correlation with prior experimental data; new interpretations for some of the nonlinear phenomena in the experimental data has also been provided based on our study. (C) 1996 Acoustical Society, of America.