Formulation of the Aeroelastic Instability Problem of Rectangular Plates in Uniform Flow Based on the Hamiltonian Mechanics for the Constrained System
Formulation of the Aeroelastic Instability Problem of Rectangular Plates in Uniform Flow Based on the Hamiltonian Mechanics for the Constrained System
复制标题
基于约束系统哈密顿力学的均匀流中矩形板气动弹性失稳问题的表述
DOI：
10.1115/pvp2014-28646
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Masahiro Watanabe
中科院分区：
文献类型：
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作者：
Kensuke Hara;Masahiro Watanabe
本文基于经典变分原理框架，提出了均匀不可压缩无旋流中板的公式和气动弹性不稳定性分析。由于板位移和速度势之间存在内在的代数关系，该系统必须被表述为约束系统。在本研究中，我们尝试将哈密顿力学应用于混合边界条件下的流固耦合问题的表述。结果，我们获得了规范方程，其中包括板位移、速度势、拉格朗日乘数和这些物理量的规范共轭动量的演化方程。特别是，人们发现拉格朗日乘子就是压力。换句话说，不仅可以推导出板块位移和速度势的时间演化方程，还可以推导出压力（拉格朗日乘数）的时间演化方程。通过特征值分析对该系统的稳定性进行了分析。然后，讨论了颤振模式、它们的频率和增长率。所提出的技术的优点是可以减少稳定性分析中的迭代过程。因此，可以预期可以有效地评估该系统的稳定性。本文介绍了唯一二维问题的表述，并以数值算例的形式实现了无夹板的稳定性分析。然而，这个公式可以应用于三维问题，而没有内在的困难。
This paper addresses a formulation and an aeroelastic instability analysis of a plate in a uniform incompressible and irrotational flow based on the classical variational principle framework. Because of an intrinsic algebraic relation between the plate displacement and the velocity potential, this system has to be formulated as the constrained system. In this study, we tried to apply the Hamiltonian mechanics to the formulation of the fluid-structure interaction problem with mixed boundary condition. As a result, we obtain the canonical equations, that consist of the evolution equations for the plate displacement, the velocity potential, the Lagrange multiplier and canonically conjugate momenta for those physical quantities. In particular, it was found that the Lagrange multiplier was just the pressure. In other words, the equations of time evolution could be derived for not only the plate displacement and the velocity potential but also the pressure (the Lagrange multiplier). The stability of this system was analyzed by the eigenvalue analysis. Then, flutter modes, their frequencies and growth rates were discussed. The proposed technique has the advantage that it can reduce iteration procedures in the stability analysis. As a consequence, it can be expected that the stability of this system can be evaluated efficiently. This paper introduces a formulation of the only two dimensional problem, and the stability analysis of a clamped-free plate is implemented as an numerical example. Howerver, this formulation can be applied to three dimensional problems without intrinsic difficulties.