The DIMM Tower Modal Study
(short summary of a preliminary analysis study)

Scope of study: Reduction of DIMM Tower amplitude under wind load.
Measure: Improvement of DIMM Tower Stiffness and increase of eigenfrequency.

By: Franz Koch, ESO Garching, October 1998

1. Measurement Results:

Eigenfrequency Measurements on Paranal (2.8.98) resulted in lowest eigenfrequency in horizontal direction of 6.9 and 7.5 Hz

2. Finite Element Analyses

2.1 Existing DIMM Tower Structure

FE Model (dimm_1.*) of existing DIMM tower structure was built according to design drawings from OAC (No. 34712-34720).

Analysis Assumptions:

- Approximate weight of DIMM telescope 150 kg located at 150 cm above top of platform.

- 171 nodes, 175 elements (ANSYS beam, pipe and lumped mass elements)

- DIMM Tower Joints modelled with beam elements. Appropriate rotational DOF released.

- Mass of telescope as lumped mass

- all 6 DOFs fixed at 4 Interface Personnel Tower/Foundations (DRW 34720)
Results:

Total Mass: 773 kg

CoG_z: 3.433 m above ground

equivalent stiffness of tower (horizontal): k = 1.056 kN/mm

lowest horizontal eigenfrequency: f = 7.5 Hz

2.2 Improved DIMM Tower Structure by added "wire cables"

FE Model (dimm_2.*) is equivalent to the existing DIMM tower FE Model (dimm_1.*) except:

- 4 aditional preloaded wire cables (steel) connect the top tower joints with the bottom flanges of the personnel tower columns.

- Non-linear "tension-only" spar elements with initial strain capability used to simulate the preloaded wire cables (static analysis).

- Modal analysis performed by using the changed stiffness matrix of the preloaded static analysis (ANSYS PRESTRESS option).

Results:

Total Mass: 795 kg (Variant 7)

CoG_z: 3.397 m from ground (Variant 7)

various configurations calculated:

______________________________________________________________________
    
Variant  Wire Cable   Wire Cable      horizontal       horizontal  
 No.      Diameter     Preload      tower stiffness   eigenfrequency
            [mm]      [mm]    [kN]     [kN/mm]            [Hz]          
______________________________________________________________________

 1            8        10      17        1.86             10.1  
 2            8        15      25.6      1.86             10.1  
 3           12        15      56.7      2.8              12.1  
 4           16        10      65.9      3.9              13.9  
 5           16        20     131.7      3.9              13.7  
 6           20        10     100.4      5.1              14.9 
 7           20         5      50.2      5.1              15.3 
 8           20         2      20.1      5.1              15.4 
______________________________________________________________________

In order to maintain the increased tower stiffness (see table above), ALL wire cables shall see tension forces > 0 under all operational conditions. The worst operational condition is obviously when the tower and telescope is exposed to the wind. The maximum wind load during operational conditions are estimated to be as follows:

Fw = Ap * cw * rho * 0.5 * v**2 = 925 N.

whereas

Cross sectionial Area exposed to the wind: Ap = 2 m**2

Drag Coefficient: cw = 3

Air Density at 2600 m altitude: rho = 0.952 kg/m**3

maximum wind speed: v = 18 m/s

In order to be conservative a horizontal load of 10000 N was applied to the DIMM telescope in the static analyses. In all cases the minimum force in the cables was well above 0 N. Further optimisation of the preload force can be done, when a more detailed design is available, i.e. wire cable diameter and connections selected or using tubes instead of wire cables.

2.3 Improved DIMM Tower Structure by "welded Joints"

Since the tower stiffness is quite sensitive to the structural behaviour of the bolted joints, it is proposed to weld each of the 16 joints pairs together (see sketch from M. Kraus, 6.10.98). In this case also any possible play can be eliminated. The following FE Analysis simulates this configuration. In addition, the tower foundation structure is added to the model.

The new FE Model (dimm_3.*) is equivalent to the existing DIMM tower FE Model (dimm_1.*) except:

- adequate model of the 16 "welded Joints" by beam elements and

- adequate model of the tower foundation structure by 3D solid elements

- all degrees of freedom fixed at bottom of foundation

The FE Model (dimm_3.db) comprises 5515 elements and 6176 nodes.

Results:

Steel structure Mass: 1312 kg

Foundation structure Mass: 21505 kg

Total Mass: 22817 kg

The horizontal stiffness of the tower when exposed to wind loads is calculated to be 2.264 kN/mm. Hence, the stiffness and amplitude can be improved by a factor of 2.14 compared to the existing structure (dimm_1.*).

The lowest eigenfrequency in horizontal direction is calculated to be 10 Hz, which is a factor 1.33 better than the existing tower. The eigenfrequency in rotational direction about the vertical z-axis is calculated to be 15.3 Hz.

2.4 Conclusions

The lowest eigenfrequency (7.5 Hz) and mode shape of the measured DIMM Tower structure agrees very well with the FE Model analysis result of the existing tower structure (dimm_1.*). In order to improve the tower stiffness, preloaded wire cables have been added to the structure.
According to the structural analysis presented before, the introduction of 4 preloaded wire cables leads to a significant improvement of the existing DIMM Tower performance. Depending on the diameter and the preload of the wire cables, the stiffness can be improved by factors between 1.7 to 4.8 and the eigenfrequencies by factors between 1.3 to 2.1

Alternatively, an easy way to improve the structural tower performance is to weld the 16 bolted pairs of "joints" together. With this measure, the stiffness and amplitude can be improved by a factor of 2.1 and the lowest eigenfrequency by a factor of 1.3 to 10 Hz.

Nevertheless, if further improvement of the tower structure is required, it can be done by adding tubes or wire cables appropriately.

3 Plot files

3.1 Plots of the existing DIMM Tower structure (OAC design)

FE model
FE model
modal results:
1st Mode shape, translation in x (7.5 Hz)
2nd Mode shape, translation in x (7.5 Hz)
3rd Mode shape, rotation about z-axis (15.9 Hz)

3.2 Plots of the improved (reinforced) DIMM Tower structure

FE model
FE model
FE model
FE model
modal results:
1st Mode shape, translation in x (15.3 Hz)
2nd Mode shape, translation in y (15.3 Hz)
3rd Mode shape, rotation about z-axis (15.4 Hz)
static results under horizontal load of Fx=10000 N:
Tensile Stresses [N/m^2] in the wire cables under Fx=10000 N
Von Mises Stresses [N/m^2] in the tubes under Fx=10000 N
Maximum Stresses [N/m^2] in the joints and top plate beams under Fx=10000 N

3.3 Plots of the improved (welded joints) DIMM Tower structure

FE model
FE model
FE model
FE model
modal results:
1st Mode shape, translation in x (10 Hz)
2nd Mode shape, translation in y (10 Hz)
3rd Mode shape, rotation about z-axis (15.3 Hz)
4th Mode shape, bending of hollow tubes (22.6 Hz)
static results under horizontal load of Fx=10000 N:
Displacement Plot, u_max = 4.4 mm
Von Mises Stress plot, sig_max = 15.6 MPa
Von Mises Stress plot, detail sig_max = 15.6 MPa
Maximum Stress plot of joints and top frame , sig_max = 33.1 MPa
Von Mises Stress plot of the hollow tubes , sig_max = 25.1 MPa

The DIMM Tower Modal Study (short summary of a preliminary analysis study)