Date of Award


Publication Type

Doctoral Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering


Engineering, Mechanical.




The torsional vibration characteristics of a geared system with clearance are investigated in this study. The clearance results in a bilinear restoring force characteristic which is non-linear in nature. This particular type of non-linearity causes the generation of ultraharmonic, harmonic and subharmonic resonances. Analytical solutions are derived for ultraharmonic, harmonic and subharmonic resonances by the application of the Ritz averaging method with two or three term approximations for forcing functions of the type T cos (omega)t and C (omega)('2) cos (omega)t. T and C are constants and (omega) is the forcing frequency. The accuracy of this approximate method is verified by means of analog computer simulation. The analytical solutions agree quite closely with analog computer results. The analytical solutions are also compared with experimental results obtained from a mechanical model with a bilinear restoring force characteristic. The mechanical model exhibits ultraharmonic and harmonic resonances, but fails to develop distinct subharmonic resonances owing to inadequate power capacity of the vibrator system used. With the analog computer however, the subharmonic resonance is excited over a limited frequency range. Although the experimental results are lower in magnitude than predicted, they distinctly show the nature of non-linear response. The theory of limiting conditions for the generation of subharmonic resonances is developed in Appendix IV.Dept. of Mechanical, Automotive, and Materials Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1983 .J378. Source: Dissertation Abstracts International, Volume: 44-09, Section: B, page: 2864. Thesis (Ph.D.)--University of Windsor (Canada), 1983.