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On Equations of Motion of Elastic Linkages by FEM

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  • Michał Hać

Abstract

Discussion on equations of motion of planar flexible mechanisms is presented in this paper. The finite element method (FEM) is used for obtaining vibrational analysis of links. In derivation of dynamic equations it is commonly assumed that the shape function of elastic motion can represent rigid-body motion. In this paper, in contrast to this assumption, a model of the shape function specifically dedicated to the rigid-body motion is presented, and its influence on elastic motion is included in equations of motion; the inertia matrix related to the rigid-body acceleration vector depends on both shape functions of the elastic and rigid elements. The numerical calculations are conducted in order to determine the influence of the assumed shape function for rigid-body motion on the vibration of links in the case of closed-loop and open-loop mechanisms. The results of numerical simulation show that for transient analysis and for some specific conditions (e.g., starting range, open-loop mechanisms) the influence of assumed shape functions on vibration response can be quite significant.

Suggested Citation

  • Michał Hać, 2013. "On Equations of Motion of Elastic Linkages by FEM," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-10, April.
    • Handle: RePEc:hin:jnlmpe:648706
    DOI: 10.1155/2013/648706
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