Dynamic modeling and analysis of large-scale antenna structure
Shen Longa, Gong Zhenbanga, Liu Lianga, Luo Shengb, Yang Shilianga a School of Mechatronics and Automation, Shanghai Univer
sity, 200072; b School of Mechatronics Engineering, Wenzhou University, 325035
In order to do the systematical dynamic modeling and analysis of the Ku-band 16meter antenna satellite ground station used a satellite telecommunication, We calculated the eigenvalues of the the Ku-band 16meter antenna structure, and used the SAP5, a large structure analysis software, to do the finite element calculation and analysis. The first ten band eigenvalues of the antenna structure were calculated; And the results showed that the minimum natural frequency was 2.075 Hz. Furthermore, based on National Military Standard, we measured the system frequency of the Ku-band 16meter antenna satellite ground station and got the minimum natural frequency of 2.249Hz. So there is quite good agreement between the theoretical minimum natural frequency (2.075 Hz) and the measuring minimum natural frequency (2.249Hz). This shows that dynamic modeling and analysis of a large-scale antenna structure system is effective. Keywords: antenna, antenna structure, dynamic analysis, dynamic modeling, model analysis
The project of the Ku-band 16meter antenna satellite ground station consists of two parts: a Ku-band 16meter antenna system and its antenna tower base. And the entire project which is complex and gigantic consists of the following parts: The large-scale antenna structure system and its tower base, the frequency conversion equipments, the demodulation equipments, the demultiplexers, the signal processing equipments, and the terminal equipments. Also the structure of this project is very large and complicated, and it refers to lots of subjects, such as mechanical structure, building structure, base structure and so on. The traditional dynamic analysis method is restricted by a lot of factors such as computer memory, calculation speed, seizing time and so on. To solve this problem, we can simplify the system to a Multi-DOF Vibration (M-K) system by the method of lumping mass. This method was commonly used. For example, in China in 1970s, a 30meter antenna ground station system of wheel & track type was introduced from USA (used in the No.1 earth station of international satellite in Beijing), and In 1990s, a 32meter antenna ground station system of wheel & track type was introduced from Japan (used in the No.9 earth station of international satellite in Beijing); In 1980s, we developed a high accuracy 20meter antenna ground station system, and we hold the fully knowledge property right (this production gained the 1st. prize of the national science & technology progress of the P.R.China in 1987) . The above systems all used the method of lumping mass to make a dynamic analysis and calculation. On the other hand, with the developments of computer technology and mechanics analysis theory, the SAP5, a FEA software which is world known, is used to take a dynamic analysis to the entire 16meter antenna system(including the antenna tower base) of The project of the Ku-band 16meter antenna satellite ground station. It’s true that there have been some difficulties in describing the dynamic model when we use the FEA theory to analyze the large antenna ground station. Because not only the original data is very abundant and so the calculation task is fussy, but also the mode shape of the system contains a lot of local shapes (which makes it hard to have a modal analysis, because modeling analysis, engineering practice and our experience is required.) However, comparing with the method of lumping mass and the method of FEA, the latter has many obvious advantages, such as higher calculation precision and the modal eigenvalue solution will be not easy to lose.
2. DYNAMIC MODELING
The project of the Ku-band 16meter antenna satellite ground station consists of the following three parts: the antenna reflector (including the system structure of feed), the antenna pedestal, and the tower base. Depending on practical force
Fifth International Symposium on Instrumentation Science and Technology, edited by Jiubin Tan, Xianfang Wen, Proc. of SPIE Vol. 7133, 713310 ? 2009 SPIE CCC code: 0277-786X/09/$18 · doi: 10.1117/12.808385 Proc. of SPIE Vol. 7133 713310-1
condition in each part, a dynamic modeling is carried out. 853 notes are chosen in the whole system. And the element type includes: beam element, bar element, membrane element, shell element, and boundary element. In all, there are 1639 elements in the dynamic model of the antenna system . 2.1 Unit division and selection (1) The Part of Antenna Reflector (991 elements divided into 7 sets The assistant transmitter and the supporting structure of focusing equipment is described as a second element (beam element), because the assistant transmitter and supporting structure not only bear a tensile and compressive strength but also have a moment capacity. The main transmitter panel and the structure of the adjusting supporting pedestal is connected in the same supporting pedestal by adjusting screw (number of 4 or 2). So there is a joint stiffness in the structure. Moreover, there is a minim movable clearance in radial and tangential direction using to have a little adjusting. Because of this special structure, and after modeling, simulation, and testing, we simplify the main transmitter panel and its adjusting supporting pedestal as a third element (membrane element). Though this membrane element can’t bear the in-plane tensile and compressive load, it can bear a few in-plane shear loads. The back-structure is the main structure of the spatial structure. Though a spatial moment capacity is required in whole, tensile capacity is needed instead of moment capacity when it refers to each beam. So the beam of the back-structure can be simplified to be a bar element in order to simplify the mathematic model. The central part and balance weight is described as a sixth element (shell elements) because not only an in-plane load bearing is required but also a moment capacity is needed. (2) The Part of Antenna Pedestal (324 elements, divided into 9 sets) This part is described as second elements and sixth elements, because both tensile, compressive strength and moment capacity is required in the main antenna framework and the main load-bearing platform. The structure such as assistant platform, armchair, and helicoidal stairs are given a concentrated loads processing. (3) The Part of Antenna Tower Base (324 elements, divided into 9 sets) The antenna tower base consists of two parts: the base and the tower. The tower is of reinforced concrete structures#200, and it can bear tensile, compressive, and normal loads. So the tower structure is described as a combination of the second elements and the sixth elements. The base consists of 8 pile foundations (diameter of 600cm and depth of 19.5) which is of reinforced concrete#300 . 2.2 Boundary conditions The nodes of the 8 foundation are simplified as a hinged supports (X=Y=Z=0) and the other nodes are simplified as movable hinged supports (Y=0). As the base foundation consist of 8 reinforced concrete pile foundations (#300, diameter of 600cm and depth of 19.5), and the earth around the foundation is hard . 2.3 Load processing The system deadweight is automatically formed by computer. The lumped mass includes sub-reflector focusing equipment, feed subsystem, pitching gearwheel, helicoidal stairs, AZ and EL drive devices and so on. And the concentrated loads infliction to each lumped mass are realized by proper methods, such as method of lumped mass distribution element, method of assistant element infliction, and method of changing element density. 2.4 Decision of operating condition The system dynamic character of the antenna in any posture is described by the EL. mode shape (when antenna face the sky, EL=90?) and the AZ. mode shape (when antenna point to horizon, EL=0?). Now we take a dynamic analysis calculation to these two basic shapes. And the first ten bands eigenvalues of the antenna system is calculated. (shown in Table 1, Table 2) (1)The EL. mode shape when antenna face the sky (EL=90? . (2)The AZ. mode shape when antenna point to horizon (EL=0? .
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3. VALUE CALCULATION AND MODEL ANALYSIS
3.1 The EL. mode shape when antenna face the sky (EL=90?)
Table 1. The EL. mode shape when antenna face the Sky
MODE NUMBER 1 2 3 4 5 6 7 8 9 10
CIRCULAR FREQENCY (RAD/SEC) 0.1304E+02 0.1675E+02 0.1852E+02 0.4529 E+02 0.4973 E+02 0.5177 E+02 0.5636 E+02 0.5661 E+02 0.6657 E+02 0.7624 E+02
FREQENCY (CYCLES/SEC) 0.2075E+01 0.2666 E+01 0.2948 E+01 0.7208 E+01 0.7915 E+01 0.8240 E+01 0.8970 E+01 0.9009 E+01 0.1059 E+02 0.1213 E+02
PERIOD (SEC) 0.4819E+00 0.3751 E+00 0.3392 E+00 0.1387 E+00 0.1263 E+00 0.1214 E+00 0.1115 E+00 0.1110 E+00 0.9439 E-01 0.8242 E-01
TOLERANCE 0.3343E-15 0.2026 E-15 0.1657 E-15 0.1774 E-14 0.1663 E-13 0.0000 E+00 0.5726 E-15 0.5677 E-15 0.2481 E-12 0.8840 E-12
Based on shape picture and model analysis, we find that: the first natural frequency of EL. mode shape is 2.075Hz. The shape picture can be seen in following pictures (Fig.1 to Fig.5). For the lack of article length, only the first five shape pictures are listed.
Fig. 1. The mode shape of EL. EL=90? f 1= 2.075 Hz
Fig. 2. The mode shape of EL. EL=90? f 2= 2.666 Hz
Fig. 3. The mode shape of EL. EL=90? f 3= 2.948 Hz
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Fig. 4. The mode shape of EL. EL=90? f 4= 7.208 Hz
Fig. 5. The mode shape of EL. EL=90? f 5= 7.915 Hz
3.2 The AZ. mode shape when antenna point to horizon (EL=0?
Table 2. The AZ. mode shape when antenna point to horizon
MODE NUMBER 1 2 3 4 5 6 7 8 9 10
CIRCULAR FREQENCY (RAD/SEC) 0.1377E+02 0.1687E+02 0.2086E+02 0.3357 E+02 0.4249 E+02 0.4973 E+02 0.5637 E+02 0.5693 E+02 0.6494 E+02 0.7741 E+02
FREQENCY (CYCLES/SEC) 0.2191E+01 0.2684 E+01 0.3319 E+01 0.5343 E+01 0.6762 E+01 0.7915 E+01 0.8971 E+01 0.9061 E+01 0.1034 E+02 0.1232 E+02
PERIOD (SEC) 0.4564E+00 0.3725 E+00 0.3013 E+00 0.1872 E+00 0.1479 E+00 0.1263 E+00 0.1115 E+00 0.1104 E+00 0.8117 E+00 0.8117 E+00
TOLERANCE 0.4498E-15 0.5995 E-15 0.7842 E-15 0.1134 E-14 0.2004 E-13 0.2004 E-13 0.1718 E-14 0.8418 E+15 0.5752 E-13 0.5752 E-13
Based on shape picture and model analysis, we find that: the first natural frequency of target AZ. mode shape is 2.191Hz. The shape picture can be seen in following pictures (Fig.6 to Fig.10). For the lack of article length, only the first five shape pictures are listed.
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Fig. 6. The mode shape of AZ. EL=0? f 1= 2.191 Hz
Fig. 7. The mode shape of AZ. EL=0? f 2= 2.684 Hz
Fig. 8.The mode shape of AZ. EL=0? f 3= 3.319 Hz
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Fig. 9. The mode shape of AZ. EL=0? f 4= 5.343 Hz
Fig. 10. The mode shape of AZ. EL=0? f 5= 6.762 Hz
Thus, combine with the two kinds of modal analysis, we get the lowest natural frequency: 2.075Hz.
4. ENGINEERING MEASUREMENTS TO NATURAL FREQUENCY OF THE ANTENNA
In engineering, there are two methods to measure the natural frequency of steel structure and architecture structure: Micro-vibration Measuring Method and External Disturbance Measuring Method. These two methods are different in the way of local oscillator disturbance and in the response of system structure. Micro-vibration Measuring Method: Through interior vibration source of system structure, get the micro-vibration in different frequency, and also get the response spectrum of the system structure in different frequency. After analyzing the frequency response, finally get the natural frequency of each band. This method can easily measure the resonant frequency of the system local-structure. External Disturbance Measuring Method: Through exterior vibration source of system structure, get the micro-vibration in different frequency, and also get the response spectrum of the system structure in different frequency. After analyzing
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frequency response, finally get the natural frequency of each band. This method can get each system resonant frequency of the macro-structure. Moreover, it well eliminates the non-main local resonant. According to the People's Republic of China National Military Standard (GJB2521-95) (Appendix B: “Measurement method to antenna resonant frequency,”) we actually take the External Disturbance Measuring Method, which can measure the resonant frequencies in macro. After field measurement according to the People's Republic of China National Military Standard (GJB2521-95), we get the minimum natural frequency of the entire antenna system: 2.249Hz .
5. ERROR CALCULATIONS AND ANALYSIS
To this engineering antenna system, after theoretical calculation, the minimum natural frequency is 2.075Hz. And the measuring minimum natural frequency is 2.249Hz. So, the absolute error of theoretical calculation is -0.174Hz, and the relative error is about 8.4% which is below 10% meeting the technology requirements of engineering analysis.
By dynamic modeling and analysis of the Ku-band 16meter antenna satellite ground station equipped in the project of a satellite telecommunication, each resonant frequency is gained. After a model analysis we get the minimum natural frequency of the entire antenna system: 2.075 Hz. And after the measure of the natural frequency of the antenna scene system, we get the minimum natural frequency of the antenna system: 2.249Hz. So we can see that the relative error of this two natural frequency only 8.4% which is lower than 10% the tolerable relative error in engineering. This shows that dynamics modeling analysis and calculation to large-scale antenna structure is effective and feasible. Thus, we refer to this conclusion: dynamic analysis modeling and calculation to a large-scale antenna structure is one of an important theoretical basis on designing and determining the development scheme to the large-scale antenna structure. It has been verified by practical application of engineering that the method of modeling analysis referred in this paper are useful in theory and have important application value in engineering.
This research was jointly sponsored by State Leading Academic Discipline Fund and Shanghai Leading Academic Discipline (Project No.Y102 and BB67), which are greatly appreciated by the authors.
  
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