Dynamics analysis of linear elastic planar mechanisms

Jin Fan Liu, Jingzhou Yang, Karim Abdel-Malek

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

This paper presents a formulation for the dynamics analysis of an elastic mechanism and integrating a stiff system using efficient numerical methods. Because all the elastic degrees of freedom are included in the vector of generalized variables, the size of the equations is much larger than that obtained using either the assumed mode or the distributed parameter finite element approach. However, the resulting system matrix is sparse and the elastic coordinates are absent from the system matrix, and these are useful properties for subsequent numerical analysis. Techniques for solving a system of linear time-variant equations are applied to the dynamics equations, assuming that the system matrix is slow-changing, and thus, may be approximated by a series of piecewise constant matrices. It is argued that the problem of determining the integration time step is transformed into the problem of computing the exponential of the system matrix with automatic time scaling. A numerical example is given to show that the behavior of the rigid coordinates converges to that of an all-rigid-body model by artificially increasing the Young's modulus of the elastic components, despite the very-high-frequency vibrations of the elastic coordinates induced by the increment of the stiffness.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalMultibody System Dynamics
Volume17
Issue number1
DOIs
StatePublished - Feb 2007

Keywords

  • Dynamic analysis
  • Hamiltonian form
  • Planar elastic mechanisms
  • Stiff system

Fingerprint Dive into the research topics of 'Dynamics analysis of linear elastic planar mechanisms'. Together they form a unique fingerprint.

Cite this