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

Abstract

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

Keywords

Timoshenko beam / geometrically exact formulation / large transformation / Lagrangian coordinates / Hamiltonian mechanics / Poisson brackets

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