Stability of Elastic Multi-Link Structures

1. Auflage 2022
ISBN: 978-3-030-86350-0
Verlag: Springer International Publishing

Buch, Englisch, 141 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 242 g

Reihe: SpringerBriefs in Mathematics

This brief investigates the asymptotic behavior of some PDEs on networks. The structures considered consist of finitely interconnected flexible elements such as strings and beams (or combinations thereof), distributed along a planar network. Such study is motivated by the need for engineers to eliminate vibrations in some dynamical structures consisting of elastic bodies, coupled in the form of chain or graph such as pipelines and bridges. 
There are other complicated examples in the automotive industry, aircraft and space vehicles, containing rather than strings and beams, plates and shells. These multi-body structures are often complicated, and the mathematical models describing their evolution are quite complex. For the sake of simplicity, this volume considers only 1-d networks.

Zielgruppe

Research

Autoren/Hrsg.

Shel, Farhat

Ammari, Kaïs

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik

Inhaltsverzeichnis

1. Preliminaries.- 2. Exponential stability of a network of elastic and thermoelastic materials.- 3. Exponential stability of a network of beams.- 4. Stability of a tree-shaped network of strings and beams.- 5. Feedback stabilization of a simplified model of fluid-structure interaction on a tree.- 6. Stability of a graph of strings with local Kelvin-Voigt damping.- Bibliography.