Timoshenko beam under finite and dynamic transformations: Lagrangian coordinates and Hamiltonian structures

2024/07/19 by Cosserat, Oscar, Marrec, Loïc Le · 1 citation
#37K58 #37N15 #70H09 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2407.14453

Abstract

In the framework of Timoshenko beam, the material parameters are inherently prescribed on the material moving frame. In this regard, we derive the strong and weak formulations of the dynamics under finite transformation in Lagrangian coordinates. Accordingly, analytical mechanics tools are used to deduce a new Hamiltonian formulation of the model which proves to be remarkably simple and synthetic.

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• Geometric theory of generalised continua using moving frames

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