LAUSR

Abstract 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.