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Semi-Analytical Study of Separation and Re-contact of a Moving Oscillator on a Rectangular Plate under Accelerating and Decelerating Motion

Rahmani, Amir Reza | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57876 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Foyouzat, Mohammad Ali
  7. Abstract:
  8. This study investigates the dynamics of a two-mass oscillator travelling on a viscoelastic rectangular plate under both accelerating/decelerating and uniform motions, while accounting for surface roughness and various reattachment scenarios. Despite its practical significance, this topic has received limited attention in scholarly literature. The Current article studies how key parameters—including the oscillator’s initial velocity, acceleration, foundation/oscillator damping and stiffness, as well as impact type (elastic, plastic, and elastoplastic)—affect the system’s dynamic response. It also examines, via illustrative examples, the oscillator’s motion along paths parallel and diagonal to the plate’s edge, highlighting the significance of the rectilinear path. In contrast, at low to moderate initial velocities, the restitution coefficient plays a critical role in determining the system’s response. However, when the initial velocity exceeds a certain threshold, the plate response is not significantly affected by the considered type of impact. The study also distinguishes between accelerating/decelerating and uniform motions, finding that the decelerating motion generally results in greater responses at lower initial velocities. The number of consecutive reattachments of the oscillator to the plate is also examined. Furthermore, the results emphasize the significant influence of surface roughness on the system's performance, particularly during decelerating motion and in cases where the foundation exhibits high stiffness and damping. The present study derives the equation of motion for an oscillator on a Maxwell viscoelastic plate, and then compares the responses obtained from the Maxwell plate with those from a plate with a Kelvin-Voigt model. These findings hold profound implications for civil engineering practice, particularly in the optimization of structures such as bridges, railway tracks, and airplane runways, where moving objects and impact phenomena are prevalent. The study underscores the importance of incorporating restitution coefficients, viscoelastic models, surface roughness into design strategies to enhance the safety, durability, and passenger comfort of infrastructure
  9. Keywords:
  10. Kelvin-Voigt Model ; Maxwell Equations ; Separation ; Surface Roughness ; Restitution Coefficient ; Impact ; Viscoelastic Sandwich Plate ; Oscillator Accelerating/Decelerating Motion

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