发表机构
University of Bayreuth; German Aerospace Center (DLR); Leibniz University Hannover; University of Cologne（拜罗伊特大学; 德国航空航天中心; 汉诺威莱布尼茨大学; 科隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种针对含Kelvin-Voigt阻尼的内禀梁模型的能量稳定不连续伽辽金空间离散方法，通过将截面合力分解为弹性和粘性部分，结合特征迎风与交替辅助迹线实现半离散能量稳定性，并在Julia框架中实现与验证。
AI 中文摘要
我们提出了一种针对含Kelvin-Voigt阻尼的内禀梁方程的能量稳定不连续伽辽金（DG）空间离散格式。通过将总截面合力分解为弹性部分和粘性部分，我们对控制方程进行了重构，从而得到一个不含混合时空导数的混合系统。对于齐次悬臂边界条件，连续系统满足能量耗散恒等式。结合特征迎风与交替辅助迹线，所提出的DG离散格式在所陈述的齐次分裂边界闭合条件下在半离散层面是能量稳定的。该方法已在基于Julia的仿真框架this http URL中实现。一个所有状态和粘性分量均被激活的物理相容的制造解用于评估收敛性，而一个旋转梁测试则验证了解析常自旋分支以及受驱动的能量平衡。
英文摘要
We present an energy-stable discontinuous Galerkin (DG) spatial discretization of the intrinsic beam equations with Kelvin-Voigt damping. We reformulate the governing equations by splitting the total sectional resultants into elastic and viscous parts, thereby exposing a mixed system without mixed space-time derivatives. For homogeneous cantilever boundary data, the continuous system obeys an energy dissipation identity. With characteristic upwinding and alternating auxiliary traces the DG discretization is energy stable at the semidiscrete level for the stated homogeneous split boundary closure. The method is implemented in the Julia-based simulation framework Trixi.jl. A physically compatible manufactured solution with all state and viscous components active assesses convergence, while a rotating-beam test verifies the analytic constant-spin branch and the actuated energy balance.
Comments37 pages, 2 figures. Submitted to Journal of Computational Physics
