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Theoretical and Experimental Analysis of a Three Dimensional Timoshenko Beam on a Moving Base

Kakavand, Farshad | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44359 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Zohoor, Hassan
  7. Abstract:
  8. In this thesis, the equations of motion of a beam with tip mass on flying support, based on Euler-Bernoulli and Timoshenko beam theories is derived. To attempt for having accurate model in high rotational speeds, stretch variable is considered and employed in the equations of motion. For a planar and a spatial rotating beam, equations of motion are lineralized and simulated. Finite Element Method and Newmark direct integration scheme are employed for the analysis of the governing equations. To support the numerical results, an experimental setup is designed and based on which different tests are performed. A cantilever beam on a flying support free to vibrate in three dimensions is considered. Modal characteristics and frequency response of the beam are investigated and measured. Experimental findings and numerical results are compared and good agreement is observed, and indication of the validity and correct approach in the theoretical concept.A further investigation on the end effector and joints motion of a double link flexible manipulator is performed. For the prescribed motion, Timoshenko and Euler-Bernoulli beam models are employed. Using Galerkin method nonlinear equations of motion are solved. Rung-kutta method is employed for time response integration. A comparative study is made between the Euler-Bernoulli and Timoshenko beam models with and without stretch effect. It is demonstrated both models namely Timoshenko and Euler-Bernoulli results in very close agreement at different slenderness ratios. Findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a remarkable difference between the models considering stretch variable effect and un-stiffened models in linear models. It is obvious that for high precision applications, the stiffened Timoshenko model is suitable. It is also interesting to note that torques at the joints for the entire range of slenderness ratios are the same
  9. Keywords:
  10. Flexible Robot ; Euler-Bernoulli Beam ; Timoshenko Beams ; Flying Support ; Stretch

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