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arXiv · 2412.06185

Analysis of an Inelastic Contact Problem for the Damped Wave Equation

Boris Muha·Srđan Trifunović
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Abstract

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 $\frac1\varepsilon\chi_{\{\eta<0\}} (\partial_t\eta)^-$. The weak solution exhibits well-controlled energy dissipation, occurring only during contact on a set of zero measure and exclusively 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.

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Boris Muha, Srđan Trifunović. 2024-12-09. Analysis of an Inelastic Contact Problem for the Damped Wave Equation. https://arxiv.org/abs/2412.06185

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