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Dynamic responses of a rectangular plate under motion of an oscillator using a semi-analytical method

Ghafoori, E ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1177/1077546309358957
  3. Abstract:
  4. A semi-analytical method is presented to calculate the dynamic responses of a rectangular plate due to a moving oscillator. In previous analytical solutions of the moving oscillator problem, the elastic distributed structure has usually been modeled by an elastic beam structure. This restrictive assumption is removed in this study by assuming a general plate as two-dimensional elastic distributed structure. The method can be applied for any arbitrary path on the plate. A combination of the Fourier and Laplace transformation as well as the convolution theorem is used to solve the governing differential equations of the problem. A modified integration technique is then presented to solve the coupled governing differential equations of motion. An adaptive finite element model of the system has been developed. In order to avoid the inaccurate results of the off-nodal position of the moving object, an adaptive mesh strategy is developed, thus the finite element mesh is ceaselessly adapted to follow the moving object trajectory. Illustrative examples are then shown for three different paths. Comparisons between the simulation results of the presented semi-analytical method, for specific cases, with the results of the adaptive mesh finite element method and also with the available results in the literature demonstrate the validity of the methodology
  5. Keywords:
  6. Dynamic response ; Finite element method ; Moving mass ; Moving oscillator ; Rectangular plate ; Adaptive finite element ; Adaptive meshes ; Analytical solutions ; Convolution theorems ; Distributed structures ; Elastic beam ; Finite Element ; Finite element meshes ; Fourier ; Governing differential equations ; Illustrative examples ; Integration techniques ; Laplace transformations ; Moving object trajectories ; Moving objects ; Moving oscillators ; Rectangular plates ; Semi-analytical methods ; Simulation result ; Convolution ; Equations of motion ; Laplace transforms ; Oscillators (mechanical) ; Plates (structural components)
  7. Source: JVC/Journal of Vibration and Control ; Volume 17, Issue 9 , 2011 , Pages 1310-1324 ; 10775463 (ISSN)
  8. URL: http://jvc.sagepub.com/content/17/9/1310.abstract