移动容器中液体晃动的二种速度势描述及其等价性证明

Two Velocity Potential Descriptions for Fluid Sloshing in Moving Tanks and Their Equivalence Proof

不同的工程学科采用二种不同的速度势函数来描述运动容器中理想流体的晃动,所得到的运动方程不尽相同,然而这二个速度势不加区分地都称为“速度势函数”,这会给跨学科的研究带来理论上的混乱,这一问题在现有文献中似乎并未得到澄清。本文采用“相对速度势”与“绝对速度势”分别建立了运动容器中液体的晃动方程,证明了二种速度势方程的等价性,对于地震工程而言,“绝对速度势”与“相对速度势”分别适用于容器的地震激励为速度与加速度的情形。

In the existing literature, there were two different velocity potential functions being used in the different engineering disciplines for describing the motions of ideal fluid in the moving tanks. The resulting equations of motion were not identical. However, the two different velocity potentials were both called “velocity potential function” in the different engineering disciplines. It might result in a theoretical confusion in the interdisciplinary researches. This issue seemed not being clarified in the existing literatures. This paper will respectively propose the “absolute velocity potential” and the “relative velocity potential” to establish the motion equations of fluid, and prove the equivalence of the two descriptions. For the earthquake engineering, the “absolute velocity poten-tial” and “relative velocity potential” are respectively suitable for describing the motions of fluids subjected to velocity and acceleration (seismic) excitations.