- Email: [email protected]
Free vibration studies on typical large flexible spacecraft appendages under vacuum conditions
Mech. Much. l'heo O" Vol. 24. No, 6. pp. 481--492, 1989 Printed in Great Britain
0094-114X89 $3,00 + 0.00 Pergamon Press plc
FREE VIBRATION STUDIES ON TYPICAL LARGE FLEXIBLE SPACECRAFT APPENDAGES UNDER VACUUM CONDITIONS C. V. R. REDDY,It T. S. KRISHNAMURTHY, ~ S. HARANATH: and T. N. SURESH" ~Structures Division, ISRO Satellite Centre, Bangalore-560 017 and -'Department of Mechanical Engineering, B.M.S. College of Engineering, Bangalore-560 019, India
Abstract--This paper deals with theoretical and exoerimental investigations on the free vibration characteristics of representative large flexible solar array appendages used in spacecrafts under vacuum environmental conditions prevailing in space. Eight different configurations of solar panels with varied flexibility and surface area have been studied. The theoretical results, namely the modal parameters, have been correlated with results from experiments. These are performed on solar arrays of different configurations under varied parameters of panel flexibility, vacuum and amplitudes of vibration,
1. I N T R O D U C T I O N
Present day communication and earth observation satellites call for large flexible appendages like solar arrays, reflectors etc., for meeting the requirements of higher electrical power as well as to handle large number of communication channels. In such spacecrafts, the manoeuvres given for correcting orbit, orientation, attitude, etc., can easily excite the flexible appendages, though the disturbances are small. These disturbances are transferred to the spacecraft as angular momentum, destabilising the control system. This becomes quite critical for spacecrafts requiring high pointing accuracies, jitter etc.[l]. In order to account for the flexibilities of such large spacecraft appendages, estimation of the dynamic characteristics become very important as these properties are integrated with the control system dynamics for evaluating the performance of the control system. The accuracies of the control system and its performance depend on how accurately the appendage dynamic characteristics are estimated. With this background, an attempt has been made in the present study to estimate the free vibration characteristics of large flexible solar array appendages under vacuum conditions prevailing in space.
1. I. Damping of flexible appendages The damping of flexible appendages under vacuum environment prevailing in space is an important parameter to be estimated. Though accurate analytical tools are available to extract the frequencies and the associated mode shapes, damping estimation to date relies on experimental data. Literature, on damping measurements in orbit, reveals damping values of significantly lower magnitudes as compared to those estimated on ground[2]. These effects have been studied experimentally under atmospheric and vacuum environments.
1.2. Description of solar panels under study The representative flexible appendage chosen for theoretical and experimental study is a solar array. It is a honeycomb sandwich construction on to which the solar cells are mounted. Each panel in the array is 1.3 m long and 1.1 m wide and weighs about 7.0 kg. The total thickness of the panel is 25.4 mm comprising of 25 mm thick aluminium honeycomb core having a density of 26 kg/m 3 and two aluminium face sheets, of 0.2 mm thickness each. Provisions are made on the panel so that one more additional honeycomb panel having the same configuration as described above can
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be attached to it. The connections between these panels, after the deployment, are rigid. Stiffeners are provided along the two longitudinal edges of the panel(s). These stiffeners are of 25.4 mm square aluminium tubes having a thickness of 1.6 mm. The panel is attached to the spacecraft through a yoke. Yoke has the sectional properties which are same as the longitudinal stiffeners. The yoke and the panel are connected through spring loaded mechanisms and on deployment the connection between the yoke and panel becomes rigid. Additional panels are constructed and attached to the solar panels in the transverse direction. These are attached only to increase the sweeping area for producing additional air drag as the structure is vibrated in atmosphere and help in studying the effect of air drag on damping. The additional panels are constructed using aluminium frames of channel cross section with a web of 25.4 mm, flanges of 12.7 mm with a thickness of 3.2 mm. These panels are 1.2 m long and 0.8 m wide and are covered with a thin polythene membrane to realise additional air drag. These are attached to the main honeycomb panel rigidly along longitudinal direction at three specified locations as shown in Fig. 3. Eight different configurations are built up with the solar panels and are shown in Fig. 1. Theoretical study was performed for all the configurations to estimate the natural frequencies and associated mode shapes. Except for configurations 1, 2, 3 and 5, the rest were studied experimentally. 2. THEORETICAL STUDY The theoretical study consists of two parts, first part dealing with the estimation of natural frequencies and mode shapes using finite element techniques and the second part dealing with the estimation of damping caused due to air drag for the first mode using the analytically obtained mode shape and experimentally measured tip displacement.
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2. I. Finite element formulation and analysis In the present study, ASKA software is used for obtaining natural frequencies and mode shapes. The first step in any finite element analysis is the discretization. Appropriate elements are chosen to model various elements of the solar array assembly from ASKA element library[3]. The honeycomb panels are idealized by warped shell elements (QUAD4S) with zero warpage. This is a four noded element with 6 degrees of freedom (d.o.f.) at each node as shown in Fig. 2a. The element chosen takes into account the shear modulus of the core and this value, of the core used in the actual construction of the panel, is given as a parameter. The panel is idealized by regular rectangular elements with a good aspect ratio of 1.48 which makes the model more realistic for the honeycomb panel (see Fig. 3). The yoke and the edge stiffeners are modelled using beam elements (BECOS, BECOSX). These are two noded elements with 6 d.o.f, at each node as shown Fig. 2b. For modelling the yoke, the element without eccentricity (BECOS) is used where as eccentric connections are provided for the
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edge stiffeners as the nodal line (middle plane of the plate elements) and the line joining the centroids of the beam elements are different. Further, the joints between the yoke and the panel and that in between the panels, are also idealized by beam elements with suitable section properties as shown in Fig. 2. The additional panels (to produce more drag) are idealized only with beam elements and are attached to the main panel at specific locations. A typical finite element mesh for single panel configuration along with the type of joint connections is shown in Fig. 3. In the analysis, the fundamental frequency of the solar array depends heavily on the modelling of the root assembly. It is essential that the frequency and the mode shape of the first mode are estimated exactly, as these informations are used in estimating the air drag. The modelling of the root assembly used for the analysis is arrived at after several iterations, varying the fixity points and flexibility of the yoke. Consistent mass is used for generating the inertial property of the assembly. Since the interest in the study is to extract modal parameters and estimate the damping due to air drag using the fundamental mode shape, condensation is resorted to in reducing the problem size and hence the computational efforts. For all the plate elements, the in-plane translational d.o.f, are condensed out and only one out-of-plane displacement and two rotational d.o.f, are retained. This reduction carried out does not pose any problem to the solution accuracy as the in-plane and out-of-plane
Vibration studies on spacecraft Table I. Natural frequencies(in Hz) and damping due to air drag Conf./Mode 1 2 3 4 5 6 I Mode 1.20 1.23 I. 10 0.59 0.54 0.50 I! Mode 2.30 2.28 1.90 5.10 2.15 1.80 11I Mode 4.50 4.51 2.50 6.70 4.40 2.40 tV Mode 7.20 7.23 4.50 18.40 5.34 4.30 Damping due to air drag (%) 0.019 -0.032 0.141 -0.229
485
7 0.49 1.80 2.30 2.50 0.222
8 0.48 1.70 2.30 2.30 0.227
motion of the panel are in general decoupled, the latter being weaker. Eigen value extraction is done through N A T M O D processor available in ASKA, which tridiagonalizes the dynamic matrix and uses an inverse iteration to obtain the vectors. 2.1. I. Analytical results of the modal parameters. The natural frequencies obtained from analysis are given in Table 1 for different configurations of the solar panel assembly. The mode shapes associated with these frequencies are shown in Figs 4 and 5 corresponding to the first two modes for all configurations. It is clear from the above figures that the first mode is always a fiexural mode and the second torsional. The third and fourth modes correspond to either second flexure or combination of second flexure with torsion along lateral direction depending on whether additional frames are attached or not. 2.2. Estimation of damping due to air drag Any structure moving in a stationary fluid, experiences some resistance to its motion. This resistance, which damps the motion, depends on the velocity of the motion, density of the fluid and the surface area of the structure. For a particular medium and structure, damping force is proportional to the square of the velocity, for large velocities[4]. With this assumption, the equivalent viscous damping estimated from basic aerodynamic principles for a single d.o.f, system can be written as[5], 4
Ceq=-~Cd'pS" y . m
(1)
where p is the density of the fluid, S is the sweeping surface area, Y is the amplitude of motion, Cd is coefficient of drag and co is the natural frequency. Cd is a factor which depends on the Reynolds number and varies from zero to a finite value as the structure vibrates in a fluid. For approximate calculations, Co can be assumed to be a constant for a particular range of Reynolds numbers experienced by the structure at relatively large amplitudes[6]. The corresponding damping ratio E is given by, E = C~ 2into
(2)
where m is the mass associated with the mode of vibration. Thus we have, 2
E = 3"rim" Cd'p" S" Y
(3)
In the numerical computation of the damping ratio, the panel is discretised into a number of elements along its length and the displacement of individual elements corresponding to the fundamental mode along with the surface area and modal mass are summed up after considering Cd to be 2. The estimated air damping values for the fundamental mode of vibration are given in Table 1. It may be noted that for all the panel configurations, a tip displacement of 28 mm is considered for damping estimation, where as, a tip displacement of only 13 mm is considered for the single panel configuration.
3. E X P E R I M E N T A L
WORK
Free vibration tests are performed under atmospheric and at different vacuum conditions in the 4 m thermo-vacuum facility at ISRO Satellite Centre, Bangalore. A maximum vacuum level of 10 -5
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tort could be attained in the vacuum chamber which can accommodate a specimen of 3.5 m diameter and a height of 3.7 m. A photograph of the experimental test setup is shown in Fig. 6. A schematic view of the experimental setup is shown in the Fig. 7. The solar panels having different configurations are attached to a heavy welded mild steel fixture and hung from top, simulating the interface boundaries of the yoke mounting assembly as shown in Fig. 8. The actuating and release mechanism, shown in Fig. 9, is embeded in the test setup at 665 mm below the interface plane. The electric actuator pulls the panel till the tip deflection reaches a predetermined value (which can be varied) and releases the panel instantaneously for it to execute free oscillations. The responses of the panel are picked up by strain gauges and piezo-resistive accelerometers at locations shown in Fig. 7. These responses are recorded on an instrumentation tape recorder and analysed off-line for extracting free vibration parameters namely, frequency and damping. Tests are performed on different configurations at varied vacuum levels and tip deflections, Table 2 gives the frequencies and damping for different configurations corresponding to the fundamental mode under atmospheric and vacuum conditions (10 -3 torr).The results are presented in two ranges of tip displacements. Figures 10 and 11 show typical decay curves for configurations 4 and 8 respectively. 4. DISCUSSION OF RESULTS AND C O N C L U S I O N S The results of the theoretical and experimental studies are presented earlier in Sections 2 and 3. The theoretical estimates, of the natural frequencies and damping due to air drag, are compared with those measured in the tests and are given in Table 3. It is clear from the table that the theoretical results, of frequencies and damping due to air drag, compare well with experimental
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results. Though the free vibration parameters are estimated for all configurations in the analysis, conclusions have been drawn based on the results for configurations having two panels with and without the additional frame(s) housed with polythene sheets. It is observed from the test results that, in either ranges of panel tip displacements, the damping does not change with increase in the surface area under atmospheric conditions. On the other hand, the results clearly show a monotonic decrease in the damping ratio, contrary to expectations, for lower amplitude ranges. This decrease is partly due to increase in the natural frequency of the system under vacuum, though this cannot explain the decrease in t o t e . Following conclusions have been drawn from the study. (1) The damping is high at larger amplitudes (tip displacement of 10-25 mm) and small at lower amplitudes. There is about 40% increase in the measured damping at larger amplitudes as • 10-z
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TalSie 2. Experimental resUlts Natural frequency (Hz)
Damping ratio (%)
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Tip displacement range (mm)
Atmospheric
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2.66 1.14
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2.62 1.03
2.36 0.99
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2.62 1.10
2.37 0.88
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2.66 1.09
2.38 0.79
Table 3. Correlation of theoretical and experimental results Theory
Experiment
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Damping due to air drag (%)
Natural frequency (Hz)
Damping due to air drag ~ (%)
4 6 7 8
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0.14 0.23 0.22 0.23
0.62 0.52 0.5t 0.52
0.13 0.26 0.25 0.28
"Damping due to air drag is the difference in the damping values between measurements in atmosphere and vacuum (10-3 torr).
compared to those at smaller amplitudes. This trend is similar to that reported in [5] based on ground tests performed on the solar array of communication technology satellite as well as the results of on-orbit tests performed in space[2]. (2) Test results indicate reduced damping under vacuum conditions as compared to those under atmospheric conditions. This reduction is appreciable only up to a vacuum level of about 1 torr. Further evacuation does not produce significant decrease in damping. This confirms the results of the study reported in [4]. (3) There is a good correlation between theoretical and experimental results of damping due to air drag for the configurations studied. Further, configurations having additional panels show up an increase in damping due to air drag by about 6 0 0 as against two panel configuration without additional frames. (4) The fundamental frequency of the panels decrease with increase in size of the flexible appendage for the same root flexibility. (5) There is a reduction in the fundamental frequency by about 15% when additional frame(s) is attached. This reduction is not appreciable whether one or more frames are attached. (6) Within the range of displacements considered in the experiments, the fundamental frequency decreases as the amplitudes of vibration increase. This is partly due to increased damping at higher amplitudes added to nonlinearities in the panels. (7) The fundamental frequency of the panel under vacuum is higher by 6 to 10% as compared to those measured under atmospheric conditions. The results of the study clearly indicate that the on-orbit damping values for large flexible appendages can be estimated with reasonable accuracy from the damping values estimated in the ground tests after incorporating corrections due to air drag forces. Acknowledgements--The authors would like to put on record the wholehearted support extended by the Facilitiesand Integration Divisions of ISRO SatelliteCentre in the successfulcompletion of the work. They would like to thank in particular,M r B. N. Baliga and M r (3. Kullan, of ETF and M r Venkata Rao and T. L. Danabalan of S.I.D. for extending theirsupport. They would liketo thank M r A. V. Patki,Group Director,MS(3 and Dr P. S. Nair, Head, StructuresDivision for their encouragement and support.
492
C . V . R . REDOY et al.
REFERENCES I. J. H. Hedgerpeth, Critical requirements for the design of large space structures, ,.3ad AIAA Conf. on Large Space Platforms, Feb. 2--4 (1981). 2. R. W. Schock, Solar panel flight dynamic experiment, NASA-TP-2598 (1986). 3. ASKA User ar:d Programmer Manuals, ASKA Users Digest vol. I and 2, IKO- Software Service, GmBH (1983). 4. W. E. Baker et al., Int. J. Mech. Sci. 9, 743-766 (1967), 5. T. D. Harrison et al., Functional and dynamic testing of the flexible solar array for the communications technology satellite, 8th Conf. on Space Simulation, NASA-SP-379 (1975~. 6. R. D. Blevins, Flow Induced Vibrations, Van Nostrand Reinhold, New York (1977).
R6sum6--Cet article traite de l'6tude th6orique et exp6rimentale des caract~ristiques des vibrations libres d'aceessoires de grande dimension utilis6s pour retenir des panneaux solaires aux satellites, dans les conditions de vide rencontr6es dans l'espace. Huit configurations ayant des flexibilit6s et des dimensions diff6rentes furent &udi6es. Les r6sultats th6oriques, en particulier les modes de vibrations, furent confront6s aux r6sultats exp~rimentaux, Ces essais furent r6alis~s sous diff~rentes conditions de vide et d'amplitude de vibration. La flexibilit6 des panneuax 6tait aussi un des param&res d'essais.
0094-114X89 $3,00 + 0.00 Pergamon Press plc
FREE VIBRATION STUDIES ON TYPICAL LARGE FLEXIBLE SPACECRAFT APPENDAGES UNDER VACUUM CONDITIONS C. V. R. REDDY,It T. S. KRISHNAMURTHY, ~ S. HARANATH: and T. N. SURESH" ~Structures Division, ISRO Satellite Centre, Bangalore-560 017 and -'Department of Mechanical Engineering, B.M.S. College of Engineering, Bangalore-560 019, India
Abstract--This paper deals with theoretical and exoerimental investigations on the free vibration characteristics of representative large flexible solar array appendages used in spacecrafts under vacuum environmental conditions prevailing in space. Eight different configurations of solar panels with varied flexibility and surface area have been studied. The theoretical results, namely the modal parameters, have been correlated with results from experiments. These are performed on solar arrays of different configurations under varied parameters of panel flexibility, vacuum and amplitudes of vibration,
1. I N T R O D U C T I O N
Present day communication and earth observation satellites call for large flexible appendages like solar arrays, reflectors etc., for meeting the requirements of higher electrical power as well as to handle large number of communication channels. In such spacecrafts, the manoeuvres given for correcting orbit, orientation, attitude, etc., can easily excite the flexible appendages, though the disturbances are small. These disturbances are transferred to the spacecraft as angular momentum, destabilising the control system. This becomes quite critical for spacecrafts requiring high pointing accuracies, jitter etc.[l]. In order to account for the flexibilities of such large spacecraft appendages, estimation of the dynamic characteristics become very important as these properties are integrated with the control system dynamics for evaluating the performance of the control system. The accuracies of the control system and its performance depend on how accurately the appendage dynamic characteristics are estimated. With this background, an attempt has been made in the present study to estimate the free vibration characteristics of large flexible solar array appendages under vacuum conditions prevailing in space.
1. I. Damping of flexible appendages The damping of flexible appendages under vacuum environment prevailing in space is an important parameter to be estimated. Though accurate analytical tools are available to extract the frequencies and the associated mode shapes, damping estimation to date relies on experimental data. Literature, on damping measurements in orbit, reveals damping values of significantly lower magnitudes as compared to those estimated on ground[2]. These effects have been studied experimentally under atmospheric and vacuum environments.
1.2. Description of solar panels under study The representative flexible appendage chosen for theoretical and experimental study is a solar array. It is a honeycomb sandwich construction on to which the solar cells are mounted. Each panel in the array is 1.3 m long and 1.1 m wide and weighs about 7.0 kg. The total thickness of the panel is 25.4 mm comprising of 25 mm thick aluminium honeycomb core having a density of 26 kg/m 3 and two aluminium face sheets, of 0.2 mm thickness each. Provisions are made on the panel so that one more additional honeycomb panel having the same configuration as described above can
tTo whom all correspondence should be addressed. 481
482
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be attached to it. The connections between these panels, after the deployment, are rigid. Stiffeners are provided along the two longitudinal edges of the panel(s). These stiffeners are of 25.4 mm square aluminium tubes having a thickness of 1.6 mm. The panel is attached to the spacecraft through a yoke. Yoke has the sectional properties which are same as the longitudinal stiffeners. The yoke and the panel are connected through spring loaded mechanisms and on deployment the connection between the yoke and panel becomes rigid. Additional panels are constructed and attached to the solar panels in the transverse direction. These are attached only to increase the sweeping area for producing additional air drag as the structure is vibrated in atmosphere and help in studying the effect of air drag on damping. The additional panels are constructed using aluminium frames of channel cross section with a web of 25.4 mm, flanges of 12.7 mm with a thickness of 3.2 mm. These panels are 1.2 m long and 0.8 m wide and are covered with a thin polythene membrane to realise additional air drag. These are attached to the main honeycomb panel rigidly along longitudinal direction at three specified locations as shown in Fig. 3. Eight different configurations are built up with the solar panels and are shown in Fig. 1. Theoretical study was performed for all the configurations to estimate the natural frequencies and associated mode shapes. Except for configurations 1, 2, 3 and 5, the rest were studied experimentally. 2. THEORETICAL STUDY The theoretical study consists of two parts, first part dealing with the estimation of natural frequencies and mode shapes using finite element techniques and the second part dealing with the estimation of damping caused due to air drag for the first mode using the analytically obtained mode shape and experimentally measured tip displacement.
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2. I. Finite element formulation and analysis In the present study, ASKA software is used for obtaining natural frequencies and mode shapes. The first step in any finite element analysis is the discretization. Appropriate elements are chosen to model various elements of the solar array assembly from ASKA element library[3]. The honeycomb panels are idealized by warped shell elements (QUAD4S) with zero warpage. This is a four noded element with 6 degrees of freedom (d.o.f.) at each node as shown in Fig. 2a. The element chosen takes into account the shear modulus of the core and this value, of the core used in the actual construction of the panel, is given as a parameter. The panel is idealized by regular rectangular elements with a good aspect ratio of 1.48 which makes the model more realistic for the honeycomb panel (see Fig. 3). The yoke and the edge stiffeners are modelled using beam elements (BECOS, BECOSX). These are two noded elements with 6 d.o.f, at each node as shown Fig. 2b. For modelling the yoke, the element without eccentricity (BECOS) is used where as eccentric connections are provided for the
484
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REDDY et al.
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A, B - RIGID CONNECTIONS Fig. 3. Finite element mesh for a single panel configuration.
edge stiffeners as the nodal line (middle plane of the plate elements) and the line joining the centroids of the beam elements are different. Further, the joints between the yoke and the panel and that in between the panels, are also idealized by beam elements with suitable section properties as shown in Fig. 2. The additional panels (to produce more drag) are idealized only with beam elements and are attached to the main panel at specific locations. A typical finite element mesh for single panel configuration along with the type of joint connections is shown in Fig. 3. In the analysis, the fundamental frequency of the solar array depends heavily on the modelling of the root assembly. It is essential that the frequency and the mode shape of the first mode are estimated exactly, as these informations are used in estimating the air drag. The modelling of the root assembly used for the analysis is arrived at after several iterations, varying the fixity points and flexibility of the yoke. Consistent mass is used for generating the inertial property of the assembly. Since the interest in the study is to extract modal parameters and estimate the damping due to air drag using the fundamental mode shape, condensation is resorted to in reducing the problem size and hence the computational efforts. For all the plate elements, the in-plane translational d.o.f, are condensed out and only one out-of-plane displacement and two rotational d.o.f, are retained. This reduction carried out does not pose any problem to the solution accuracy as the in-plane and out-of-plane
Vibration studies on spacecraft Table I. Natural frequencies(in Hz) and damping due to air drag Conf./Mode 1 2 3 4 5 6 I Mode 1.20 1.23 I. 10 0.59 0.54 0.50 I! Mode 2.30 2.28 1.90 5.10 2.15 1.80 11I Mode 4.50 4.51 2.50 6.70 4.40 2.40 tV Mode 7.20 7.23 4.50 18.40 5.34 4.30 Damping due to air drag (%) 0.019 -0.032 0.141 -0.229
485
7 0.49 1.80 2.30 2.50 0.222
8 0.48 1.70 2.30 2.30 0.227
motion of the panel are in general decoupled, the latter being weaker. Eigen value extraction is done through N A T M O D processor available in ASKA, which tridiagonalizes the dynamic matrix and uses an inverse iteration to obtain the vectors. 2.1. I. Analytical results of the modal parameters. The natural frequencies obtained from analysis are given in Table 1 for different configurations of the solar panel assembly. The mode shapes associated with these frequencies are shown in Figs 4 and 5 corresponding to the first two modes for all configurations. It is clear from the above figures that the first mode is always a fiexural mode and the second torsional. The third and fourth modes correspond to either second flexure or combination of second flexure with torsion along lateral direction depending on whether additional frames are attached or not. 2.2. Estimation of damping due to air drag Any structure moving in a stationary fluid, experiences some resistance to its motion. This resistance, which damps the motion, depends on the velocity of the motion, density of the fluid and the surface area of the structure. For a particular medium and structure, damping force is proportional to the square of the velocity, for large velocities[4]. With this assumption, the equivalent viscous damping estimated from basic aerodynamic principles for a single d.o.f, system can be written as[5], 4
Ceq=-~Cd'pS" y . m
(1)
where p is the density of the fluid, S is the sweeping surface area, Y is the amplitude of motion, Cd is coefficient of drag and co is the natural frequency. Cd is a factor which depends on the Reynolds number and varies from zero to a finite value as the structure vibrates in a fluid. For approximate calculations, Co can be assumed to be a constant for a particular range of Reynolds numbers experienced by the structure at relatively large amplitudes[6]. The corresponding damping ratio E is given by, E = C~ 2into
(2)
where m is the mass associated with the mode of vibration. Thus we have, 2
E = 3"rim" Cd'p" S" Y
(3)
In the numerical computation of the damping ratio, the panel is discretised into a number of elements along its length and the displacement of individual elements corresponding to the fundamental mode along with the surface area and modal mass are summed up after considering Cd to be 2. The estimated air damping values for the fundamental mode of vibration are given in Table 1. It may be noted that for all the panel configurations, a tip displacement of 28 mm is considered for damping estimation, where as, a tip displacement of only 13 mm is considered for the single panel configuration.
3. E X P E R I M E N T A L
WORK
Free vibration tests are performed under atmospheric and at different vacuum conditions in the 4 m thermo-vacuum facility at ISRO Satellite Centre, Bangalore. A maximum vacuum level of 10 -5
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Fig. 4. Mode shapes for configurations 1-4.
Vibration studies on spacecraft
487
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Vibration studies on spacecraft
489
tort could be attained in the vacuum chamber which can accommodate a specimen of 3.5 m diameter and a height of 3.7 m. A photograph of the experimental test setup is shown in Fig. 6. A schematic view of the experimental setup is shown in the Fig. 7. The solar panels having different configurations are attached to a heavy welded mild steel fixture and hung from top, simulating the interface boundaries of the yoke mounting assembly as shown in Fig. 8. The actuating and release mechanism, shown in Fig. 9, is embeded in the test setup at 665 mm below the interface plane. The electric actuator pulls the panel till the tip deflection reaches a predetermined value (which can be varied) and releases the panel instantaneously for it to execute free oscillations. The responses of the panel are picked up by strain gauges and piezo-resistive accelerometers at locations shown in Fig. 7. These responses are recorded on an instrumentation tape recorder and analysed off-line for extracting free vibration parameters namely, frequency and damping. Tests are performed on different configurations at varied vacuum levels and tip deflections, Table 2 gives the frequencies and damping for different configurations corresponding to the fundamental mode under atmospheric and vacuum conditions (10 -3 torr).The results are presented in two ranges of tip displacements. Figures 10 and 11 show typical decay curves for configurations 4 and 8 respectively. 4. DISCUSSION OF RESULTS AND C O N C L U S I O N S The results of the theoretical and experimental studies are presented earlier in Sections 2 and 3. The theoretical estimates, of the natural frequencies and damping due to air drag, are compared with those measured in the tests and are given in Table 3. It is clear from the table that the theoretical results, of frequencies and damping due to air drag, compare well with experimental
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Fig. 8. Pictorial view of the test setup.
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results. Though the free vibration parameters are estimated for all configurations in the analysis, conclusions have been drawn based on the results for configurations having two panels with and without the additional frame(s) housed with polythene sheets. It is observed from the test results that, in either ranges of panel tip displacements, the damping does not change with increase in the surface area under atmospheric conditions. On the other hand, the results clearly show a monotonic decrease in the damping ratio, contrary to expectations, for lower amplitude ranges. This decrease is partly due to increase in the natural frequency of the system under vacuum, though this cannot explain the decrease in t o t e . Following conclusions have been drawn from the study. (1) The damping is high at larger amplitudes (tip displacement of 10-25 mm) and small at lower amplitudes. There is about 40% increase in the measured damping at larger amplitudes as • 10-z
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Fig. I1. Free vibration decay curves for configuration 8.
Vibration studies on spacecraft
491
TalSie 2. Experimental resUlts Natural frequency (Hz)
Damping ratio (%)
Conf.
Tip displacement range (mm)
Atmospheric
Vacuum
Atmospheric
Vacuum
4.
10-25 5-10
0.62 0.66
0.66 0.70
2.66 1.14
2.53 1.07
6.
10-25 5-10
0.52 0.54
0.58 0.61
2.62 1.03
2.36 0.99
7.
10-25 5-10
0.51 0.53
0.58 0.61
2.62 1.10
2.37 0.88
8.
10-25 5-10
0.52 0.52
0.58 0.61
2.66 1.09
2.38 0.79
Table 3. Correlation of theoretical and experimental results Theory
Experiment
Conf.
Natural frequency (Hz)
Damping due to air drag (%)
Natural frequency (Hz)
Damping due to air drag ~ (%)
4 6 7 8
0.59 0.50 0.49 0.48
0.14 0.23 0.22 0.23
0.62 0.52 0.5t 0.52
0.13 0.26 0.25 0.28
"Damping due to air drag is the difference in the damping values between measurements in atmosphere and vacuum (10-3 torr).
compared to those at smaller amplitudes. This trend is similar to that reported in [5] based on ground tests performed on the solar array of communication technology satellite as well as the results of on-orbit tests performed in space[2]. (2) Test results indicate reduced damping under vacuum conditions as compared to those under atmospheric conditions. This reduction is appreciable only up to a vacuum level of about 1 torr. Further evacuation does not produce significant decrease in damping. This confirms the results of the study reported in [4]. (3) There is a good correlation between theoretical and experimental results of damping due to air drag for the configurations studied. Further, configurations having additional panels show up an increase in damping due to air drag by about 6 0 0 as against two panel configuration without additional frames. (4) The fundamental frequency of the panels decrease with increase in size of the flexible appendage for the same root flexibility. (5) There is a reduction in the fundamental frequency by about 15% when additional frame(s) is attached. This reduction is not appreciable whether one or more frames are attached. (6) Within the range of displacements considered in the experiments, the fundamental frequency decreases as the amplitudes of vibration increase. This is partly due to increased damping at higher amplitudes added to nonlinearities in the panels. (7) The fundamental frequency of the panel under vacuum is higher by 6 to 10% as compared to those measured under atmospheric conditions. The results of the study clearly indicate that the on-orbit damping values for large flexible appendages can be estimated with reasonable accuracy from the damping values estimated in the ground tests after incorporating corrections due to air drag forces. Acknowledgements--The authors would like to put on record the wholehearted support extended by the Facilitiesand Integration Divisions of ISRO SatelliteCentre in the successfulcompletion of the work. They would like to thank in particular,M r B. N. Baliga and M r (3. Kullan, of ETF and M r Venkata Rao and T. L. Danabalan of S.I.D. for extending theirsupport. They would liketo thank M r A. V. Patki,Group Director,MS(3 and Dr P. S. Nair, Head, StructuresDivision for their encouragement and support.
492
C . V . R . REDOY et al.
REFERENCES I. J. H. Hedgerpeth, Critical requirements for the design of large space structures, ,.3ad AIAA Conf. on Large Space Platforms, Feb. 2--4 (1981). 2. R. W. Schock, Solar panel flight dynamic experiment, NASA-TP-2598 (1986). 3. ASKA User ar:d Programmer Manuals, ASKA Users Digest vol. I and 2, IKO- Software Service, GmBH (1983). 4. W. E. Baker et al., Int. J. Mech. Sci. 9, 743-766 (1967), 5. T. D. Harrison et al., Functional and dynamic testing of the flexible solar array for the communications technology satellite, 8th Conf. on Space Simulation, NASA-SP-379 (1975~. 6. R. D. Blevins, Flow Induced Vibrations, Van Nostrand Reinhold, New York (1977).
R6sum6--Cet article traite de l'6tude th6orique et exp6rimentale des caract~ristiques des vibrations libres d'aceessoires de grande dimension utilis6s pour retenir des panneaux solaires aux satellites, dans les conditions de vide rencontr6es dans l'espace. Huit configurations ayant des flexibilit6s et des dimensions diff6rentes furent &udi6es. Les r6sultats th6oriques, en particulier les modes de vibrations, furent confront6s aux r6sultats exp~rimentaux, Ces essais furent r6alis~s sous diff~rentes conditions de vide et d'amplitude de vibration. La flexibilit6 des panneuax 6tait aussi un des param&res d'essais.