Mathematical Problems in Engineering

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Dynamical Engineering Systems

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Volume 2005 |Article ID 982489 | https://doi.org/10.1155/MPE.2005.437

Claude-Henri Lamarque, Jérôme Bastien, Matthieu Holland, "Maximal monotone model with delay term of convolution", Mathematical Problems in Engineering, vol. 2005, Article ID 982489, 17 pages, 2005. https://doi.org/10.1155/MPE.2005.437

Maximal monotone model with delay term of convolution

Received10 Feb 2004

Abstract

Mechanical models are governed either by partial differential equations with boundary conditions and initial conditions (e.g., in the frame of continuum mechanics) or by ordinary differential equations (e.g., after discretization via Galerkin procedure or directly from the model description) with the initial conditions. In order to study dynamical behavior of mechanical systems with a finite number of degrees of freedom including nonsmooth terms (e.g., friction), we consider here problems governed by differential inclusions. To describe effects of particular constitutive laws, we add a delay term. In contrast to previous papers, we introduce delay via a Volterra kernel. We provide existence and uniqueness results by using an Euler implicit numerical scheme; then convergence with its order is established. A few numerical examples are given.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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