Structural Engineering and Mechanics

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Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam

  • Liu, Zhifeng (College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology) ;
  • Yin, Yunyao (College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology) ;
  • Wang, Feng (College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology) ;
  • Zhao, Yongsheng (College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology) ;
  • Cai, Ligang (College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology)
  • Received : 2012.10.15
  • Accepted : 2013.11.04
  • Published : 2013.12.10
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Abstract

A simulation method called modified differential transform is studied to solve the free vibration problems of uniform Euler-Bernoulli beam. First of all, the modified differential transform method is derived. Secondly, the modified differential transformation is applied to uniform Euler-Bernoulli beam free-free vibration. And then a set of differential equations are established. Through algebraic operations on these equations, we can get any natural frequency and normalized mode shape. Thirdly, the FEM is applied to obtain the numerical solutions. Finally, mode experimental method (MEM) is conducted to obtain experimental data for analysis by signal processing with LMS Test.lab Vibration testing and analysis system. Experimental data and simulation results are illustrated to be in comparison with the analytical solutions. The results show that the modified differential transform method can achieve good results in predicting the solution of such problems.

Keywords

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