Chinese Journal of Theoretical and Applied Mechani ›› 2015, Vol. 47 ›› Issue (2): 362-366.DOI: 10.6052/0459-1879-14-207

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EFFECTS OF COUPLING TERMS IN STRAIN ENERGY ON FREQUENCY OF A ROTATING CANTILEVER BEAM

Zhao Guowei1, Wu Zhigang1,2   

  1. 1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;
    2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
  • Received:2014-09-18 Revised:2014-10-31 Online:2015-03-23 Published:2014-11-02
  • Supported by:

    The project was supported by the National Natural Science Foundation of China (11072044), the Research Fund for the Doctoral Program of Higher Education (20110041130001), and the Program for New Century Excellent Talents in University (NCET-11-0054).

Abstract:

Dynamic modeling of a rotating cantilever beam is very important for dynamic characteristics analysis and controller design. In literature, the coupling terms between axial and transverse deformation in strain energy are ignored in first order approximate model. However, as shown by this paper, these terms have a significant impact on the dynamic characteristics. By discussing how to select the strain energy, this paper takes into account the coupling terms. Based on Hamilton's principle, the coupling vibration equations of the rotating cantilever beam are obtained. Using Rayleigh- Ritz method, the bending mode shapes of the beam without rotational motion are selected as basic functions to derive characteristic equation. A numerical example is presented to show that the evident difference of bending frequencies between the models with and without the coupling terms in strain energy.

Key words:

cantilever beam|rigid-flexible coupling|floating reference frame|Rayleigh&mdash, Ritz method

CLC Number: