Published 2023-09-14
Keywords
- Elastic thin plates,
- Viscoelastic boundary conditions,
- Relaxation function,
- Memory effects,
- Boundary control.
How to Cite
Copyright (c) 2023 Top Academic Journal of Engineering and Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Abstract
In this study, we investigate the behavior of elastic thin plates subject to viscoelastic boundary conditions. The plates are situated within a bounded domain in ℝ² with a smooth boundary Γ. We consider a scenario where the plate is clamped at one part of the boundary (Γ₀) and experiences memory effects on another part (Γ₁), with positive boundary measure. The vertical deflection ????(????, ????) of the thin plate is governed by a partial differential equation with specific boundary conditions. Our research addresses the following key aspects: The governing partial differential equation describing the vertical deflection of the thin plate. Boundary conditions involving clamped and memory-affected parts of the boundary. The relaxation function, which characterizes the memory effect. Boundary control functions influencing the behavior of the plate. Given initial conditions for ????(????, ????) and its time derivative ????????(????, ????). Conditions on the memory function ????(⋅) that ensure physical relevance. We delve into the mathematical foundations of this problem, addressing the challenging interplay between elasticity, memory effects, and boundary conditions. Our analysis considers the properties of the relaxation function ????(⋅) and its implications for the plate's behavior. We aim to contribute to a deeper understanding of elastic structures with viscoelastic boundary conditions and their practical applications
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