Abstract With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using active load-bearing elements integrated into the structure. Such adaptive structures are of high complexity and very heterogeneous in nature. Port-Hamiltonian systems theory provides a promising approach for their modeling and control. Subsystem dynamics can be formulated in a domain-independent way and interconnected by means of power flows. The modular approach is also suitable for robust decentralized control schemes. Starting from a distributed-parameter port-Hamiltonian formulation of beam dynamics, we show the application of an existing structure-preserving mixed finite element method to arrive at finite-dimensional approximations. In contrast to the modeling of single bodies with a single boundary, we consider complex structures composed of many simple elements interconnected at the boundary. This is analogous to the usual way of modeling civil engineering structures which has not been transferred to port-Hamiltonian systems before. A block diagram representation of the interconnected systems is used to generate coupling constraints which leads to differential algebraic equations of index one. After the elimination of algebraic constraints, systems in input-state-output (ISO) port-Hamiltonian form are obtained. Port-Hamiltonian system models for the considered class of systems can also be constructed from the mass and stiffness matrices obtained via conventional finite element methods. We show how this relates to the presented approach and discuss the differences, promoting a better understanding across engineering disciplines. A Matlab framework is available on http://github.com/awarsewa/ph_fem/ to facilitate the application of the methods to different problems.

中文翻译：

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一种模拟复杂系统结构动力学的哈密尔顿港法

摘要 通过这一贡献，我们给出了一个完整而全面的框架，用于将复杂机械结构的动力学建模为哈密尔顿系统。这是由于对使用集成到结构中的主动承重元件的轻质结构潜力的研究。这种自适应结构具有很高的复杂性并且本质上非常异构。哈密​​尔顿港系统理论为其建模和控制提供了一种很有前景的方法。子系统动力学可以以与域无关的方式制定，并通过功率流相互连接。模块化方法也适用于稳健的分散控制方案。从光束动力学的分布参数 port-Hamiltonian 公式开始，我们展示了现有结构保持混合有限元方法的应用，以获得有限维近似值。与具有单一边界的单体建模相比，我们考虑由在边界处互连的许多简单元素组成的复杂结构。这类似于以前没有转移到港口-汉密尔顿系统的土木工程结构建模的常用方法。互连系统的框图表示用于生成耦合约束，这导致索引为 1 的微分代数方程。消除代数约束后，得到输入-状态-输出（ISO）端口-哈密顿形式的系统。所考虑的系统类别的 Port-Hamiltonian 系统模型也可以从通过传统有限元方法获得的质量和刚度矩阵构建。我们展示了这与所提出的方法的关系并讨论了差异，促进了对工程学科的更好理解。http://github.com/awarsewa/ph_fem/ 上提供了一个 Matlab 框架，以方便将这些方法应用于不同的问题。