Analysis of an inelastic contact problem for the damped wave equation

In this paper, we examine the dynamic behavior of a viscoelastic string oscillating above a rigid obstacle in a one-dimensional setting, accounting for inelastic contact between the string and the obstacle. We construct a global-in-time weak solution to this problem by using an approximation method...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 86; p. 104408
Main Authors Muha, Boris, Trifunović, Srđan
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2025
Subjects
Contact mechanics
Velocity penalization
Viscoelastic string
secondary
Viscoelastic string
Velocity penalization
Contact mechanics
primary
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Summary:In this paper, we examine the dynamic behavior of a viscoelastic string oscillating above a rigid obstacle in a one-dimensional setting, accounting for inelastic contact between the string and the obstacle. We construct a global-in-time weak solution to this problem by using an approximation method that incorporates a penalizing repulsive force of the form 1ɛχ{η<0}(∂tη)−. The weak solution exhibits well-controlled energy dissipation, which occurs exclusively during contact and is concentrated on a set of zero measure, specifically when the string moves downward. Furthermore, the velocity is shown to vanish after contact in a specific weak sense. This model serves as a simplified framework for studying contact problems in fluid–structure interaction contexts.
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2025.104408