The stability analysis of a slider-crank mechanism due to the existence of two-component parametric resonance
Slider-crank mechanisms are not only important elements in mechanical engineering, but constitute also a model problem for occurence of parametric instabilities, because the coupling element of the mechanism is subject to both axial and transversal forces. In this paper the crank is modelled as a rigid rod and a coupler which is an inextensible Bernoulli-Euler beam. For constant angular velocity of the crank, the derived partial differential equations of motion of the coupler are reduced by Galerkin's method to a set of nonlinear ordinary differential equations. These are analysed by the method of multiple time scales concerning the occurence of dynamic instabilities. Special attention is given to possible effects of multi-modal interactions. Besides of its interesting analysis, the paper presents also practically important results demonstrating that due to modal interactions new domains of parametric instabilities can be found which are not present, if only a single mode reduction of the bending of the coupler beam is performed.
scientific article; zbMATH DE number 1340917