Nonlinear Forced Parametric Resonances of a Roller Chain (In a Case Where the Frequency Ratio of Forced Lateral Displacement to Tension Fluctuation is 1:1)

Chain has a heavy weight and a high tension stiffness, which are distinctive features different from those of string. This paper describes the nonlinear harmonic and parametric resonances of a roller chain stretched horizontally, 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 the left end to that of the tension fluctuation is 1:1. The vibration characteristics are computed for two kinds of chain and are compared with the ones obtained from the experiments. In particular, the effect of the chain weight upon the resulting vibrations is considered. A fine agreement between experimental and analytical results is confirmed.