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Vibration Analysis Of Rectangular Plates Coupled With Fluid

机译：流体耦合矩形板的振动分析

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摘要

The approach developed in this paper applies to vibration analysis of rectangular plates coupled with fluid. This case is representative of certain key components of complex structures used in industries such as aerospace, nuclear and naval. The plates can be totally submerged in fluid or floating on its free surface. The mathematical model for the structure is developed using a combination of the finite element method and Sanders' shell theory. The in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively. The mass and stiffness matrices are then determined by exact analytical integration. The velocity potential and Bernoulli's equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the developed structural shape function is integrated over the structure-fluid interface to assess the virtual added mass due to the fluid. Variation of fluid level is considered in the calculation of the natural frequencies. The results are in close agreement with both experimental results and theoretical results using other analytical approaches.
机译：本文开发的方法适用于与流体耦合的矩形板的振动分析。该案例代表了航空航天，核能和海军等行业中使用的复杂结构的某些关键组成部分。这些板可完全浸没在液体中或漂浮在其自由表面上。该结构的数学模型是结合有限元方法和桑德斯壳理论开发的。分别使用双线性多项式和指数函数对平面内和平面外位移分量进行建模。然后通过精确的分析积分确定质量和刚度矩阵。采用速度势和伯努利方程来表达作用在结构上的流体压力。压力表达式与已开发的结构形状函数的乘积被集成在结构-流体界面上，以评估由于流体而产生的虚拟附加质量。在计算固有频率时会考虑液位的变化。结果与使用其他分析方法的实验结果和理论结果都非常吻合。

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