耦合刚/柔多体系统的端口哈密顿建模
Port-Hamiltonian modelling of coupled rigid/flexible multibody systems
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中文总结 AI 辅助
本文构建耦合刚/柔多体系统的端口哈密顿框架，证明其调制狄拉克结构的端口哈密顿互联仍为调制狄拉克结构，并以平面运动欧拉-伯努利梁等机构例证该框架。
中文摘要 AI 辅助
我们为耦合刚/柔多体系统构建了端口哈密顿框架。刚体动力学可呈非线性，且受构型与速度约束，柔性部件则由一维空间域上的线性端口哈密顿偏微分方程描述。子系统通过边界或分布端口相互作用；柔性侧的微分算子及其定义域保持固定，状态仅通过狄拉克结构的有限维耦合分量引入依赖。我们证明，在自然满射条件下，有限维刚性子系统的调制狄拉克结构的端口哈密顿互联仍会产生调制狄拉克结构，子系统的哈密顿量相加，内部耦合功率抵消。该框架通过平面运动欧拉-伯努利梁及带柔性连杆的曲柄滑块机构得到例证。
英文摘要
We develop a port-Hamiltonian framework for coupled rigid/flexible multibody systems. The rigid dynamics may be nonlinear and subject to configuration and velocity constraints, while the flexible components are described by linear port-Hamiltonian partial differential equations on one-dimensional spatial domains. The subsystems interact through boundary or distributed ports. On the flexible side, the differential operator and its domain remain fixed, whereas state dependence enters only through finite-dimensional coupling components of the Dirac structure. We show that, under a natural surjectivity condition, the port-Hamiltonian interconnection with a modulated Dirac structure of a finite-dimensional rigid subsystem again yields a modulated Dirac structure. The Hamiltonians of the subsystems add, while the internal coupling powers cancel. The framework is illustrated by a planar moving Euler--Bernoulli beam and a slider--crank mechanism with a flexible connecting member.
