Forced vibrations of tanks partially filled with liquid under seismic load

Abstract

Cylindrical tanks partially filled with liquid are the most general type of reservoirs for oil and other chemical-dangerous agent storage. Destruction of such tanks under seismic or impulsive load can lead to negative ecological consequences. The analysis method of dynamic behavior of cylindrical tanks partially filled with liquid that are under short-time impulsive load is under consideration. The method relies on reducing the problem of determining the fluid pressure to the system of singular integral equations. The coupled problem is solved using combination BEM and FEM. Differential equations of transient problem are solved numerically by Runge-Kutta method of 4th and 5th order. Numerical investigations of forced vibrations of the cylindrical tank filled with the incompressible fluid under seismic load have been carried out.

BEM in free vibration analysis of elastic shells coupled with liquid sloshing

“…The above relations (3), (4) show that the abovementioned shell's modes of vibration must be orthonormalized with respect to the mass matrix. Let us seek Φ as a sum of two potentials 1 2      as it was proposed in [9]. Represent the potential Φ 1 as the following series expansion:…”

“…Note that the solution of boundary value problem (6) was obtained in [9]. To determine the potential  2 we have to solve the problem of fluid vibrations in the rigid vessel taking into account the gravitational force.…”

“…Numerical methods are especially useful when the geometry of the container is complicated and the sloshing in the container cannot be analytically investigated. Various approaches have been proposed to research the fluid-structure interaction problems, including the finite difference methods [2], the finite element methods [3], the boundary element methods (BEM) [5][6][7][8][9][10]. The research findings are summarized in [11].…”

“…However such 3D finite element analysis including the contained fluid is complex and extremely time consuming. In [7][8][9] authors offer the approach based on the boundary element method to the problem of free vibrations of fluidfilled shell of revolution as well as to the problem of liquid sloshing in rigid tanks.…”

Free and forced vibrations of shell structures interacting with liquid

“…Numerical methods are especially useful when the geometry of container is complicated and the sloshing in the container cannot be analytically investigated. Various approaches have been proposed to research fluid-structure interaction, including the finite difference methods [2], the finite element methods [3], the boundary element methods [4][5][6][7][8]. The research findings are summarized in [9].…”