VARIABLE STRUCTURAL CONTROL: UNRAVELING DYNAMICS IN FLEXIBLE PLATE SYSTEMS
Abstract
This article explores the dynamic behavior of elastic thin plates with viscoelastic boundary conditions, extending previous research on wave and heat equations applied to such structures. The study focuses on a bounded domain Ω ⊂ ℝ2 with a ????2-smooth boundary Γ, where the plate is clamped and exhibits memory effects on a relatively open subset Γ0 ≠ ∅ with positive boundary measure. The vertical deflection (????, ????) of the thin elastic plate is governed by a partial differential equation, accounting for memory effects and clamped conditions.
The partial differential equation governing the vertical deflection is expressed as ????????(????, ????) + Δ2????(????, ????) = 0 in Ω × ℝ+, subject to specific boundary conditions on Γ0 and Γ1. These conditions encompass both clamped constraints and memory effects, introducing integral terms that consider the history of the vertical deflection. The relaxation function and boundary control further contribute to the complexity of the model.
Throughout the investigation, the relaxation function (⋅) adheres to specific conditions, ensuring a well-defined memory behavior. These conditions include strict monotonicity, decreasing rate of memory loss, and exponential decay of the memory function. The memory function's behavior is crucial in capturing the viscoelastic properties of the material.
The article aims to provide a comprehensive understanding of the dynamic response of elastic thin plates with viscoelastic boundary conditions. By incorporating memory effects and clamped constraints, the study contributes valuable insights into the intricate interplay between material properties and structural behavior. The proposed model and its analysis pave the way for advancements in the understanding and design of viscoelastic structures.
Keywords:
Elastic Thin Plates, Viscoelastic Boundary Conditions, Memory Effects, Clamped Constraints, Dynamic ResponseDownloads
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https://doi.org/10.5281/zenodo.10555343Issue
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Copyright (c) 2024 Catherine Marie Thompson
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