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

TL;DR

This paper develops a Hamiltonian formulation for the Timoshenko beam model under finite and dynamic transformations, utilizing Lagrangian coordinates to provide a simplified and unified analytical mechanics framework.

Contribution

It introduces a novel Hamiltonian formulation of the Timoshenko beam model in Lagrangian coordinates, accommodating finite transformations.

Findings

Derived strong and weak formulations in Lagrangian coordinates.

Established a new, simplified Hamiltonian structure for the model.

Demonstrated the analytical mechanics approach's effectiveness.

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.