Natural frequencies and vibration modes of tank's protective capacitance with weld defects under axial static load

Abstract

The natural frequencies and vibration modes of tank's protective capacitance with welded joints defects under axial static load are determined in order to construct a diagnostic model and monitor of the welded joints defects propagation. Computer simulation of capacitance dynamic behavior using the computer finite element analysis system NASTRAN was performed. The design model in the form of a cylindrical thin-walled shell with allowance for belts from weld rolled sheet was built. Weld defects as two through horizontal cracks located in the welds between the first and second shell belts were presented. The crack width was equaled to the rolled sheets diameter. For assessing the effect of crack propagation on the shell dynamic characteristics the crack length increased until a single continuous crack. The defects in the form of through cracks allowed to generalize different weld defects types and predict the shell critical state. Determination of capacitance natural frequencies and vibration modes under axial static load was performed in two stages. At the first stage, the capacitance stress-strain state in a nonlinear formulation was investigated and a total stiffness matrix (linear and geometric) was formed. The nonlinear static problem as a finite element approximation of the Lagrange possible displacements principle was formulated. The Newton-Raphson stepwise loading method (Nonlinear Static) was used. The natural frequencies and vibration modes were determined by by the Lanczos method (Param Modes) on solving the eigenvalue problem. The effect of weld defects and axial static action on the capacitance dynamic characteristics was evaluated. The results showed that the presence of cracks and an their length increase reduced the values of the natural frequencies. The static action of an axial compressive load on a thin shell wall can both reduce and increase its rigidity, thereby changing its natural frequency and vibration modes. According to the authors, consideration of such a load should be present in the dynamic calculations of thin shells, especially under stochastic loads (wind, seismic, etc.).