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Nonlinear Vibrations of Inclined Timoshenko Beam on Pasternak Foundation with Moving Force

Ramezani Farani, Mostafa | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48203 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Kargarnovin, Mohammad Hossein
  7. Abstract:
  8. In the first part of this thesis, the linear and nonlinear governing differential equations of motion of an inclined Euler-Bernoulli beam are used by tacking into account the effect of beam’s mid-plane stretching. Then nonlinear coupled governing partial differential equations of vibrations by including rotation of cross section, longitudinal and transverse displacements in the Timoshenko beam theory on Pasternak foundation under the act of moving concentrated force and as wll as moving mass are drived. To do this the energy method (Hamilton’s principle) based on the large deflection theory in conjuncture with the von-Karman relations is used. These equations are solved by applying Galerkin’s method via numerical integrating methods. Furtheremore, he effects of variation of different parameters including the magnitude of the moving mass as well as equivalent concentrated moving force, the velocity and acceleration of the moving masses, beam’s inclination angle, damping ratio and elastic stiffness of foundation, module of shearing of viscouse shear layaer of foundation are considered. In addition, effect of existence of quadratic-cubic nonlinear terms in the coupled PDEsgoverning equations of motion on the dunamic response of the inclined Timoshenko beam on pastenak foundation subjected to moving mass/force investigated using both linear and nonlinear solutions
  9. Keywords:
  10. Traveling Mass ; Nonlinear Vibration ; Timoshenko Beams ; Motion Equation ; Pasternak Fundation ; Inclined Beam

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