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Free vibration analysis of flexible rectangular fluid tanks with a horizontal crack

机译：水平裂纹柔性矩形流体箱的自由振动分析

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This paper proposes a numerical approach using the Rayleigh-Ritz method for the free vibration analysis of three-dimensional flexible rectangular fluid tanks with a surface crack. A hypothetical boundary along the crack is assumed, such that it divides the steel wall of the tank into two regions. The total potential energy is obtained from the summation of the potential energy of two regions and the crack. The discontinuity in the wall is created with the local line-springs along the crack, reducing the flexural strength of the steel wall at the crack location. A set of static beam differential equations is used for the shape function of the tank-wall vibration, where the cracks are modeled along the transverse direction of these beams. The velocity potential of the liquid is estimated through the separation of variables and the superposition method. A numerical study was then conducted based on the proposed method. The results indicate that the crack reduces the natural frequencies of the steel tank. It is also worth mentioning that the calculations are performed with acceptable accuracy and low computational costs.
机译：本文提出了一种使用瑞利丽升方法的数值方法，用于具有表面裂纹的三维柔性矩形流体箱的自由振动分析。假设沿着裂缝的假设边界，使得它将罐的钢壁分成两个区域。总势能从两个区域和裂缝的潜在能量的总和获得。墙壁中的不连续性由沿裂缝的局部线弹簧产生，降低钢壁在裂缝位置的弯曲强度。一组静态光束微分方程用于罐壁振动的形状函数，其中裂缝沿着这些光束的横向建模。通过分离变量和叠加方法来估计液体的速度电位。然后基于所提出的方法进行数值研究。结果表明，裂纹减少了钢罐的固有频率。还值得一提的是，以可接受的准确性和低计算成本进行计算。

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