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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Dynamical Systems
Volume 10 - 2024 | doi: 10.3389/fams.2024.1418656
This article is part of the Research Topic Approximation Methods and Analytical Modeling Using Partial Differential Equations View all 13 articles

Qualitative properties of solutions to a nonlinear transmission problem for an elastic Bresse beam

Provisionally accepted
Tamara Fastovska Tamara Fastovska 1,2Dirk Langemann Dirk Langemann 3Iryna Ryzhkova Iryna Ryzhkova 1*
  • 1 V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
  • 2 Humboldt University of Berlin, Berlin, Baden-Wurttemberg, Germany
  • 3 Technical University of Braunschweig, Braunschweig, Lower Saxony, Germany

The final, formatted version of the article will be published soon.

    We consider a nonlinear transmission problem for a Bresse beam, which consists of two parts, damped and undamped. The mechanical damping in the damped part is present in the shear angle equation only, and the damped part may be of arbitrary positive length. We prove wellposedness of the corresponding system in energy space and establish existence of a regular global attractor under certain conditions on nonlinearities and coefficients of the damped part only. Besides we study singular limits of the problem under consideration when curvature tends to zero or curvature tends to zero and simultaneously shear moduli tend to infinity, and perform numerical modelling for these processes.

    Keywords: Bresse beam, transmission problem, Global attractor, Singular limit, PDE

    Received: 16 Apr 2024; Accepted: 02 Jul 2024.

    Copyright: © 2024 Fastovska, Langemann and Ryzhkova. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Iryna Ryzhkova, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

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