An exact three-dimensional analysis based on the linear potential theory and the elaborated method of eigenfunction expansion in elliptic coordinates are presented to study the free coupled elasto-hyrodynamic characteristics of an upright non-deformable cylindrical container of elliptical planform with a flexible bottom plate, filled to an arbitrary depth with an inviscid incompressible liquid. Extensive numerical data are presented in an orderly fashion for the first few symmetric/anti-symmetric coupled hydroelastic natural frequencies as a function of fluid depth parameter for two plate aspect ratios. Also, selected hydrodynamic and structural deformation modes shapes are presented in graphical form. The effects of liquid level, bottom plate elasticity, and cross sectional aspect ratio on the sloshing frequencies and hydrodynamic pressure modes are examined. The validity of the results is examined through computations using a commercial finite element package as well as by comparison with the data available in literature.

中文翻译：

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具有弹性底部的椭圆形圆柱罐的耦合水弹性振动

提出了一种基于线性势能理论的精确三维分析方法和精细的椭圆函数展开方法，以研究具有柔性底板的直立不可变形椭圆形平面圆柱容器的自由耦合弹性动力学特性，用无粘性的不可压缩液体填充到任意深度。对于两个板长宽比，前几个对称/反对称耦合水弹性固有频率作为流体深度参数的函数，以有序方式给出了广泛的数值数据。而且，选定的流体动力和结构变形模式的形状以图形形式呈现。液位，底板弹性，并研究了横摆长宽比对晃动频率和流体动压模的影响。通过使用商业有限元软件包进行的计算以及与文献中的可用数据进行比较，可以检验结果的有效性。