Application of the DAE approach to the nonlinear sloshing problem
Application of the DAE approach to the nonlinear sloshing problem
复制标题
DAE 方法在非线性晃动问题中的应用
DOI：
10.1007/s11071-019-05399-3
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发表时间：
2019
影响因子：
5.6
通讯作者：
Watanabe Masahiro
中科院分区：
文献类型：
--
作者：
Hara Kensuke;Watanabe Masahiro
非线性晃动问题是液体储罐、液体货物运输、可调液体阻尼器等设计的重要问题。本文致力于开发一种基于哈密顿力学的非线性晃动问题的新方法。特别是，本研究旨在开发可用于分析非线性液体表面行为（如在小液体深度中观察到的行波）的方法。在本公式中，假设流体是无粘性、不可压缩且无旋转的流动。然后，通过非线性多模态模型描述液体表面运动。然而，由于基于此类假设的晃动问题会产生不规则的拉格朗日量，因此很难以直接的方式进行公式化。因此，本方法采用约束哈密顿力学和拉格朗日待定乘子法来推导运动方程。所得系统由微分方程和代数方程组成，称为微分代数方程 (DAE)。此外，本方法充分考虑了非线性模式与模式的相互作用，而没有集中于主要晃动模式的简化方法。然而，没有这种简化方法的多模态模型会遇到严重的数值刚性问题。因此，基于隐式方案（DAE 求解器）的数值积分技术被纳入作为刚性问题的补救措施。具体而言，通过采用伽辽金法和离散导数来导出运动方程的离散形式。通过与现有模型和时域分析实验的比较，验证了所提出的方法。
The nonlinear sloshing problem is an important issue for design of liquid storage tanks, liquid cargo transportations, tuned liquid dampers and so on. This paper is concerned with development of a novel approach for the nonlinear sloshing problem based on the Hamiltonian mechanics. In particular, this study is aimed at developing the method available to analyze the nonlinear liquid surface behavior like a traveling wave observed in the small liquid depth. In the present formulation, the fluid is assumed to be inviscid incompressible and irrotational flow. Then, the liquid surface motion is described by nonlinear multimodal models. However, since the sloshing problem based on such assumptions yields an irregular Lagrangian, it makes formulation difficult in a straightforward way. Therefore, the present approach employs the constrained Hamiltonian mechanics with the Lagrange’s method of undetermined multipliers to derive equations of motion. The resulting system is comprised of differential equations and algebraic equations, referred to as differential algebraic equations (DAEs). In addition, the present method takes full account of the nonlinear mode-to-mode interactions without reduction methods focusing on the predominant sloshing modes. However, the multimodal models without such reduction methods suffer from severe numerical stiff problem. Therefore, the numerical integration techniques based on implicit schemes (DAE solver) are incorporated as remedies for the stiff problem. Specifically, discrete forms of the equations of motions are derived by employing the Galerkin method and a discrete derivative. The proposed approach is validated by comparisons with an existing model and an experiment in time domain analysis.
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DOI：
10.1098/rspa.1968.0103
发表时间：
1968-05
期刊：
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
影响因子：
--
作者：
R. Seliger;G. Whitham
通讯作者：
R. Seliger;G. Whitham
不规则储罐几何形状和小液深TLD的非线性多模态模型
影响因子：
3.6
作者：
J. Love;M. Tait
通讯作者：
M. Tait
层状两种不混溶流体非线性晃动的哈密顿公式
DOI：
10.1299/jsdd.2.1183
发表时间：
2008
期刊：
Journal of System Design and Dynamics
影响因子：
--
作者：
K. Hara;H. Takahara
通讯作者：
H. Takahara
储罐中自由表面和界面运动的哈密顿公式（系统非线性引起的 N 波共振相互作用）
DOI：
10.1299/jsdd.2.1218
发表时间：
2008
期刊：
Journal of System Design and Dynamics
影响因子：
--
作者：
K. Hara;H. Takahara
通讯作者：
H. Takahara
影响因子：
3.4
作者：
O. Bauchau
通讯作者：
O. Bauchau