Modal analysis of the protective shell of the tank taking into account the sequential occurrence of defects in the welded seams of the wall
Keywords:modal analysis, finite element method, free vibrations, nonlinear behavior, thin-walled cylindrical shell, weld defect
The natural frequencies and vibration modes of the protective shell of the fuel tank with defects in the welded seams of the wall were investigated. With the help of a computer finite element program a model of the protective container in the form of a cylindrical thin-walled shell was constructed. The wall of the shell was presented in the form of belts and surfaces that consist of the rolled sheets. Each surface was represented as a set of flat quadrangular finite elements with six degrees of freedom in each node. Defects of the welds were presented in the form of one vertical and two horizontal through cracks located in different belts of the shell. To simulate the defects at their locations flat quadrangular and triangular finite elements were used. The modal analysis of the protective shell was performed by solving the eigenvalue problem using Lanczos method. The effect of constant static vertical weight load of the roof and fencing, which is dangerous for the overall stability of the thin wall of the shell, is estimated. Determination of natural frequencies and vibration modes of the protective shell under the action of a vertical load was performed in two stages. At the first stage, the nonlinear statics problem was formulated as a modified Lagrange approach and solved using the Newton-Raphson stepwise loading method. At the second stage, the eigenfrequencies and vibration modes of the protective shell were determined using the Lanczos method. The problem of predicting the propagation of defects is solved by simulating their sequential occurrence as well as increasing their length and number.
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