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Dynamics of a Viscoelastic Plate on a Viscoelastic Foundation Subjected to a Moving Mass

Foyouzat, Mohammad Ali | 2017

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50264 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Esmaeil Purestekanchi, Homayoun; Mofid, Masoud
  7. Abstract:
  8. This thesis investigates the dynamic response of a viscoelastic plate resting on a viscoelastic Winkler foundation subjected to the excitation of a moving mass. Through application of the Laplace transform, the governing equation of the problem is derived for a general viscoelastic material. Thereafter, an analytical-numerical method is proposed in order to determine the dynamic response of the viscoelastic plate. The method is based on transforming the governing partial differential equation into a new solvable system of linear ordinary differential equations. To that extent, the proposed solution proves to be applicable to plates made of any viscoelastic material and with various boundary conditions. Moreover, the moving mass may travel at any arbitrary trajectory with no restriction. The capability of the method is demonstrated through several illustrative examples, wherein a comprehensive parametric study is performed to investigate the effect of various parameters on the response of the system. A comparison between the results obtained by the complete moving mass approach with those coming from the approximate solutions is also carried out. By exercising the abovementioned method, the current study is followed by introducing a simple analytical-numerical approach in order to examine another important problem concerned with the dynamics of plates—that is—the dynamic response of thin plates resting on multiple elastic point supports with time-varying stiffness. The formulation of this problem is closely related to that of the moving-mass problem, as in both problems the plate is acted upon by time-varying concentrated forces. Moreover, it is shown that the method can be applied to multiple-support problems just as simple as for the problems with a single support without giving rise to any significant increase in the computational cost
  9. Keywords:
  10. Viscoelastic Foundation ; Laplace Trasformation ; Kelvin-Voigt Model ; Maxwell Equations ; Moving Mass Load ; Viscoelastic Behavior ; Elastic Point-Support

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