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An investigation on effects of traveling mass with variable velocity on nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions

Mamandi, A ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijmecsci.2010.09.003
  3. Publisher: 2010
  4. Abstract:
  5. In this paper, the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a traveling mass with variable velocity is investigated. The nonlinear coupled partial differential equations of motion for the bending rotation of cross-section, longitudinal and transverse displacements are derived using Hamilton's principle. These nonlinear coupled PDEs are solved by applying Galerkin's method to obtain dynamic response of the beam under the act of a moving mass. The appropriate parametric studies by taking into account the effects of the magnitude of the traveling mass, the velocity of the traveling mass with a constant acceleration/ deceleration and effect of different beam's boundary conditions are carried out. The beams' large deflection has been captured by including the stretching effect of its mid-surface. It was seen that the existence of quadratic-cubic nonlinear terms in the governing coupled PDEs of motion renders hardening/stiffening behavior on the dynamic responses of the beam when traversed by a moving mass. In addition, the obtained nonlinear results are compared with those from the linear analysis
  6. Keywords:
  7. Inclined Timoshenko beam ; Nonlinear vibrations ; Variable velocity motion ; Galerkin's method ; Geometric non-linearity ; Non-linear vibrations ; Timoshenko beams ; Traveling mass ; Attitude control ; Boundary conditions ; Dynamic response ; Equations of motion ; Galerkin methods ; Particle beams ; Velocity ; Nonlinear equations
  8. Source: International Journal of Mechanical Sciences ; Volume 52, Issue 12 , 2010 , Pages 1694-1708 ; 00207403 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0020740310002146