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Lyapunov functions for linear damped wave equations in one-dimensional space with dynamic boundary conditions*

Abstract

This paper considers a one-dimensional wave equation on [0, 1], with dynamic boundary conditions of second order at x = 0 and x = 1, also referred to as Wentzell/Ventzel boundary conditions in the literature. In additions the wave is subjected to constant disturbance in the domain and at the boundary. This model is inspired by a real experiment. By the means of a proportional integral control, the regulation with exponential converge rate is obtained when the damping coefficient is a nowhere-vanishing function of space. The analysis is based on the determination of appropriate Lyapunov functions and some further analysis on an associated error system. The latter is proven to be exponentially stable towards an attractor. Numerical simulations on the output regulation problem and additional results on related wave equations are also provided. (c) 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

article Article

date_range 2024

language English

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Chitour Yacine

Nguyen Hoai-Minh

Roman Christophe

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One -dimensional wave equation

Wentzel boundary conditions

Regulation

Output feedback control

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Effect of corrosion on flexural strength of reinforced concrete beams with polypropylene fibers

Abstract

An experimental study was performed to investigate the effects of polypropylene fibers on uncorroded and corroded reinforced concrete beams. Three different volume fractions of polypropylene fibers having 0, 0.5, and 1.5%, were tested at four corrosion levels of 0% and approximately 5, 7, and 9%. A full scale of an accelerated corrosion pool was used for the accelerated corrosion process. Reinforced concrete beams were used for an under monotonic bending test. The contribution of the actual corrosion levels of transverse and longitudinal reinforcement bars to the total corrosion levels were obtained from reinforcement bars fully extracted from concrete. Flexural strength, bond-slip, and moment-curvature relationships were examined for uncorroded and corroded reinforced concrete beams. A new model was developed to predict the flexural strength of corroded reinforced concrete beams. The proposed model for predicting the residual flexural strength of corroded beams was compared with test data published in previous studies. Furthermore, a novel model is presented for improved predictions between the actual and theoretically estimated corrosion mass losses, based on Faraday’s law, with the aid of fully extracted reinforcement bars. The model used to predict the flexural strength of corroded reinforced concrete beams with large sizes demonstrated good agreement with current and previously published literature data. In the case of corroded beams comprising differing amounts of polypropylene fibers, the performance of the corroded beams was limited by a fiber volume fraction of 1.5% at low corrosion levels.

article Article

date_range 2018

language English

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