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On the Dynamic Response of Thin Viscoelastic Plates to a Moving Oscillator using MLSDQ as a Mesh-Free Method

Ekhlasi, Alireza | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58740 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Foyouzat, Mohammad Ali
  7. Abstract:
  8. This work introduces a powerful, general, meshless solution strategy that challenges the conventional reliance on finite element methods for such problems and redefines how such dynamic interactions are modeled. By employing the Moving Least Squares (MLS) approximation within Lagrange’s formalism, the proposed method seamlessly accommodates arbitrary boundary conditions, complex geometries, viscoelastic foundation behavior, and freely defined motion paths. The plate’s material response is captured through the Kelvin–Voigt viscoelastic model, enabling accurate representation of hereditary effects. The method’s significance, robustness and versatility are validated through rigorous numerical simulations and an extensive parametric analysis. System parameters such as oscillator mass, velocity, path curvature, and foundation damping are explored in detail. It has been shown that, in some cases, the discrepancy in the plate’s response between the moving mass model and the moving oscillator model can reach up to 100%, which must be taken into account when designing critical structures. These results illuminate the nuanced interplay between structural dynamics and viscoelastic interactions, marking a significant step forward in the simulation of oscillator-driven plate systems—offering a blueprint for future research in advanced structural dynamics
  9. Keywords:
  10. Kelvin-Voigt Model ; Moving Oscillator ; Lagrange Equation ; Meshless Method ; Thin Viscoelastic Plates ; Least Squares Method

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