Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major benefit of the PH representation is the explicit formulation of power interfaces, so-called ports, which allow for a power-preserving interconnection of subsystems to compose flexible multibody systems in a modular way. In this work, we present a PH representation of geometrically exact strings with nonlinear material behaviour. Furthermore, using structure-preserving discretization techniques a corresponding finite-dimensional PH state space model is developed. Applying mixed finite elements, the semi-discrete model retains the PH structure and the ports (pairs of velocities and forces) on the discrete level. Moreover, discrete derivatives are used in order to obtain an energy-consistent time-stepping method. The numerical properties of the newly devised model are investigated in a representative example. The developed PH state space model can be used for structure-preserving simulation and model order reduction as well as feedforward and feedback control design.

翻译：端口哈密顿系统为建模、分析和控制复杂动态系统提供了一个框架，此类系统的复杂性可能源于多物理场耦合、非平凡域以及多种非线性特性。端口哈密顿表示的主要优势在于显式地表述功率接口（即所谓的端口），这些接口允许以模块化方式通过功率守恒互联子系统来构成柔性多体系统。本文提出了具有非线性材料特性的几何精确弦的端口哈密顿表示。此外，利用保结构离散化技术，建立了相应的有限维端口哈密顿状态空间模型。通过应用混合有限元方法，半离散模型在离散层面上保留了端口哈密顿结构及端口（速度与力的配对）。同时，采用离散导数以获得能量一致的时间步进方法。通过一个代表性算例研究了新设计模型的数值特性。所开发的端口哈密顿状态空间模型可用于保结构仿真、模型降阶以及前馈与反馈控制设计。