The DIMM Tower Modal 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
______________________________________________________________________ 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.
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.
The new FE Model (dimm_3.*) is equivalent to the existing DIMM tower FE Model (dimm_1.*) except:
The FE Model (dimm_3.db) comprises 5515 elements and 6176 nodes.
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.
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.