Nonlinear response of a roller chain to combined forcing and parametric excitations (2nd report, Theoretical analysis of 1/3-harmonic and parametric combination resonance)

Abstract

This paper describes the analytical results of the nonlinear subharmonic and parametric combination resonance of a roller chain stretched vertically, which is regarded as a system with many degrees of freedom, when the elongation of the chain during vibration is taken into account. The resonance treated in this report is one of the resonances excited by combined forcing and parametric excitations in which the ratio of the frequency of the forced lateral displacement acting at a lower end to that of the tension fluctuation is 3 : 2. The vibration characteristics are computed for the chains with different frictional coefficients and are compared with the forced ones without parametric excitation. The remarkable features attributable to the combined excitations and the changes of the characteristics with friction and with degree of freedom are shown in the figures.