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Nonlinear vibrations of an inclined beam subjected to a moving load

Mamandi, A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1088/1742-6596/181/1/012094
  3. Abstract:
  4. In this paper, the nonlinear dynamic responses of an inclined pinned-pinned Euler-Bernoulli beam with a constant cross section and finite length subjected to a concentrated vertical force traveling with constant velocity is investigated by using the mode summation method. Frequency analysis of the PDE's governing equations of motion for steady-state response is studied by applying multiple scales method. The nonlinear dynamic deflections of the beam are obtained by solving two coupled nonlinear PDE's governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the numerical results are compared with those obtained from traditional linear solution. It is found that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also stability analysis of the steady-state response for the modes equations having quadratic nonlinearity is carried out and it is observed from the amplitude response curves that for the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon are predicted for the longitudinal excitation. © 2009 IOP Publishing Ltd
  5. Keywords:
  6. Amplitude response ; Constant velocities ; Cross section ; Dynamic magnification factors ; Euler bernoulli beams ; Finite length ; Frequency Analysis ; Governing equations ; Governing equations of motion ; Inclined beams ; Jump phenomenon ; Linear solution ; Moving load ; Multiple scales methods ; Non linear PDE ; Non-linear dynamic response ; Non-linear dynamics ; Non-linear vibrations ; Numerical results ; Planar motion ; Primary resonance ; Quadratic nonlinearities ; Softening effect ; Stability analysis ; Steady-state response ; Time history ; Transverse oscillation ; Traveling load ; Velocity ratio ; Vertical force ; Aircraft engines ; Control nonlinearities ; Dynamic response ; Equations of motion ; Equations of state ; Excited states ; Nonlinear analysis ; Nonlinear equations ; Vibration control ; Vibration analysis
  7. Source: Journal of Physics: Conference Series, 8 September 2009 through 10 September 2009, Cambridge ; Volume 181, Issue 1 , 2009 ; 17426588 (ISSN)
  8. URL: http://iopscience.iop.org/article/10.1088/1742-6596/181/1/012094