The dynamics of a slider-crank mechanism with an initially curved coupler under two-component parametric resonance

Abstract

The objective of this paper is to study the dynamics and dynamic instability of a slider-crank mechanism with an initially curved coupler under parametric resonance. An attention is given to the phenomena arising due to initial curvature, geometric imperfection, of a connecting rod and modal interactions produced by the existence of two-component parametric resonance. The two-component parametric resonance can occur, for example, when the fundamental frequency of the flexible part of a slider-crank mechanism is close to one-half of the excitation frequency and simultaneously the difference between the first and the second natural frequencies is near the frequency of excitation. It is known that for the case of one-component parametric resonance, an initially curved connecting rod enlarges the amplitude of fundamental mode of vibration significantly only if the motion is in the vicinity of the secondary region of instability. In other words, the initial curvature of a coupler plays no effects to the fundamental response of the system if the oscillation is near the primary region of instability. However, result of present study shows that under the condition of two-component parametric resonance, unlike the case of one-component parametric resonance, an initially curved linkage can result significant effects to the vibration of the system even if the motion is close to the primary region of instability. In addition, the result also indicates that the growth of small amplitude vibration into large motion regime occurs if vibrations arise near the boundary of stable region.