OS-V: 0460 Dynamic Behavior of a Fluid-containing Structure using MFLUID

A vertical clamped free cylindrical shell with a rigid bottom is chosen to demonstrate the applicability of the structures which are partially filled such as liquid storage tanks.

Figure 1. FE Model

Model Files

Before you begin, copy the file(s) used in this problem to your working directory.

Benchmark Model

In a preliminary calculation the natural frequencies and principal mode shapes of the dry structure (empty tank) are determined. In these calculations, the cylindrical shell is discretized with 8-noded quadrilateral shell elements, including both membrane and bending stiffness influences.

Later simulation is also performed for different filling ratios. For instance, for the filling ratios d/L = 0.5, 0.7, and 1.0 to predict and compare the wet natural frequencies of the clamped–free cylindrical shell.
  • The fluid is inviscid and incompressible. The fluid flow is a potential flow.
  • The fluid is nearly incompressible, the structural modes are below the compressible fluid modes.
  • There is no gravity effect or sloshing effect.

There is no acoustic effect involved. The modes from the structural side do not couple with the modes of the nearly incompressible fluid modes.

MFLUID is used to mimic the mass effect of an incompressible inviscid fluid in contact with a structure. It does not represent the actual mass of the fluid. There is no mesh needed for the fluid domain. The Virtual Fluid Mass represents the full coupling between acceleration and pressure at the fluid-structure interface. A dense mass matrix is generated among damp grids at the fluid-structure interface.

The material properties are:
Cylindrical Shell
Length (L)
231 mm
Radius (r)
77:25 mm
Thickness (t)
1.5 mm
The FE Model:
Plate (2D) Elements and Rigid
Cylinder Tank
Cylinder Bottom
The material:
Cylinder: Linear Material - MAT1
Young’s Modulus
Poisson's Ratio
Initial Density
Fluid (Water) Inside the Tank (using MFLUID)
1000 kg/m3


The Frequencies obtained from the Experiment and OptiStruct are obtained for the first 6 modes. You can also see that the wet natural frequencies for clamped–free cylindrical shell (Hz), are influenced by the water filling ratio. The wet natural frequencies increase with increasing number of axial modes, for a given number of circumferential modes.
Table 1. FE Model
Mode Type Half Filled Tank 70% Filled Tank Fully Filled Tank
Experimental OptiStruct Experimental OptiStruct Experimental OptiStruct
1 Axial

3 Circumference

609.4 608.0 552 542.5 388 402.0
1 Axial

2 Circumference

771.1 774.1 582 680.1 421 493.8
1 Axial

4 Circumference

908.8 903.0 789 801.7 628 629.8
1 Axial

5 Circumference

1352.8 1339.3 1196 1179.8 1027 1022.7
2 Axial

4 Circumference

1303.9 1303.0 1244 1250.6 1094 1103.8
1 Axial

1 Circumference

1654.4 1703.6 N/A 1492.0 N/A 1134.5
The mode shapes (Axial & Circumference) of the Half Filled tank are shown in Figure 2 as per the order described in Table 1.
Figure 2. Modes Shapes of Half Filled Tank
The mode shapes (Axial & Circumference) of the 70% Tank Filled are shown in Figure 3 as per the order described in Table 1.
Figure 3. Modes Shapes of 70% Tank Filled
The mode shapes (Axial & Circumference) of the Fully Filled Tank are shown in Figure 4 as per the order described in Table 1.
Figure 4. Modes Shapes of Fully Filled Tank


Mazuch T., "Natural modes and frequencies of a thin clamped–free steel cylindrical storage tank partially filled with water: FEM and Measurements, Journal of Sound and Vibration" 193, (1996) 669–69