The stability analysis of a slider-crank mechanism due to the existence of two-component parametric resonance
type: Item
instance of: scholarly article
title: The stability analysis of a slider-crank mechanism due to the existence of two-component parametric resonance
zbMATH Open document ID: 0952.74030
DOI: 10.1016/S0020-7683(98)00198-X
author: Yiming Wang
published in: International Journal of Solids and Structures
publication date: 2001-01-02T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74H55
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 70E50
Mathematics Subject Classification ID: 74H15
Mathematics Subject Classification ID: 70E60
zbMATH DE Number: 1340917
zbMATH Keywords: domains of parametric instabilities
zbMATH Keywords: Galerkin method
zbMATH Keywords: inextensible Bernoulli-Euler beam
zbMATH Keywords: method of multiple time scales
zbMATH Keywords: multi-modal interactions
zbMATH Keywords: coupler beam
reviewed by: Hans Troger
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1340917