978-1-4577-0557-1/12/$26.00 ©2012 IEEE 1The SMAP mission has not been formally approved by NASA. The decision to proceed with the mission will not occur until the completion of the National Environmental Policy Act (NEPA) process. Material in this document related to SMAP is for information purposes only. 1

Design and Performance of Astromesh Reflector Onboard Soil Moisture Active Passive Spacecraft

Mehran Mobrem1

Steve Kuehn1 Chris Spier1 Eric Slimko2

1Astro Aerospace - Northrop Grumman Aerospace Systems

6384 Via Real, Carpinteria, CA 93013

2Jet Propulsion Laboratory, California Institute of Technology 4800 Oak Grove Drive, M/S 303-422, Pasadena, CA 91109

Abstract - The Soil Moisture Active Passive1 (SMAP) instrument includes a conically scanning 6-m diameter deployable Astromesh reflector and feedhorn that rotates relative to a de-spun spacecraft at 14.6 RPM. This is the first application of a spinning Astromesh reflector. This paper describes the design and performance of the Reflector/Boom Assembly (RBA) under multiple constraints and requirements that are inherent to a spinning large flexible reflector/structure. The deployed RBA has stringent mass property control and knowledge requirements, structural natural frequency separation requirements, and all other typical ones including the antenna performance. Finally the validation of the design on the ground by analysis/test and its difficulties due to gravity are discussed.

TABLE OF CONTENTS

1. INTRODUCTION ................................................. 1 2. RBA MASS PROPERTY CONTROL .................... 3 3. RBA MASS PROPERTY KNOWLEDGE .............. 4 4. RBA DEPLOYED FREQUENCY .......................... 6 5. RBA SURFACE ACCURACY .............................. 8 6. SUMMARY ......................................................... 9 ACKNOWLEDGEMETNS ....................................... 10 REFERENCES ....................................................... 10 BIOGRAPHIES ...................................................... 10

1. INTRODUCTION The SMAP mission will provide the first three-day revisit global maps of the Earth’s soil moisture and freeze-thaw state, together termed the hydrosphere state. SMAP hydrosphere state measurements will yield a new data set that will enable science and applications users to understand processes that link the terrestrial water, energy and carbon cycles, estimate global water and energy fluxes at the land surface, quantify net carbon flux in boreal landscapes, enhance weather and climate forecast skill, and develop

improved flood prediction and drought monitoring capability [1].

The SMAP instrument is comprised of a 6-m diameter deployable Astromesh reflector and feedhorn that rotates relative to a de-spun spacecraft at 14.6 RPM. The antenna system is shared with a synthetic aperture radar operating at 1.26 GHz and a 1.41 GHz Radiometer that together provide simultaneous active and passive L-band observations of the Earth’s surface from which soil moisture and freeze/thaw state estimates are derived.

The Spun Instrument Assembly (SIA) includes a deployable Astromesh Reflector/Boom Assembly (RBA) supplied by Astro Aerospace - NGAS along with the Goddard Space Flight Center (GSFC) supplied Radiometer. A picture of the SMAP spacecraft is shown in Figure 1.

Figure 1 – SMAP Spacecraft

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Typically, a reflector is designed and built to meet the surface accuracy requirement for a static configuration. For the SMAP program, the reflector is designed for the spun configuration but is built for de-spun configuration with initial error which will be corrected when it reaches its operational spin rate of 14.6 RPM. These errors are mainly in the reflector surface pattern and tension field and boom geometry. The optimal surface tension field will be achieved at its operating spin while the surface error and pointing error due to manufacturing will be minimized. Furthermore due to a stringent daily pointing requirement of 12 millidegrees, the reflector will be manufactured with an initial pointing shift to minimize the daily pointing error. These initial errors are based on analysis with inputs from component testing such as boom stiffness and coefficient of thermal expansion measurements.

System tests are planned such as deployed reflector mass and center of gravity, un-spun surface measurement by photogrammetry, and natural frequency. The properties of the spun reflector (mass properties, surface accuracy, and natural frequency) will not be determined by tests due to the complexity of simulating a zero gravity environment.

This paper will discuss four critical characteristics of the deployed spun reflector:

1) Mass properties as designed

2) Mass properties knowledge as measured

3) Natural frequencies

4) Surface accuracy and pointing error- Manufacturing, spin, thermal, and on-orbit dynamics

Overview of Astromesh Design

The stowed and deployed configurations of the SMAP RBA are shown in Figure 2. The main components of the RBA are the Deployment Boom, Prime Batten and Reflector truss. The primary function of the Deployment Boom is to position the reflector assembly for operation. The Boom deployment is predictable and repeatable and once deployed, the Boom provides a stiff and thermally stable support for the reflector. The Boom design is derived from a previous Deployment Boom design used on the reflector for the Japanese MBSat spacecraft, and is cable driven.

Figure 2 – RBA Deployed and Stowed Configurations

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The Reflector truss is comprised of Longeron, Diagonal, and Batten tubes, as shown in a detail section in Figure 2. The Reflector structure consists of a series of truss tubes that frame the perimeter of the reflector and two networks of webs across the aperture which are tensioned by a set of springs, shown in Figure 3 [2]. The network of webs creates the Front and Rear Nets. The reflective mesh is shaped by the front set of webs into a series of triangular facets which approximate the shape of the desired parabola.

Figure 3 – Components of Reflector Truss

2. RBA MASS PROPERTY CONTROL Mass Properties Requirements

The SMAP Observatory is composed of a spun instrument section and a de-spun bus. Reaction wheels inside the bus compensate for the momentum so that the system is flown in a zero momentum state. However, in order to maintain a nadir-pointing attitude and minimize wobble around that state, the spun section mass properties must be such that the spin results in a net torque at the Observatory center of mass that is minimal. Constraining the spun static center of mass offset and the product of inertia as shown in Figure 4 accomplish this. The term in brackets is called the Spun Section Effective Product of Inertia and setting it to zero allows a family of mass properties that result in zero torque about the Observatory center of mass.

The deployed Reflector Boom Assembly contributes significantly to the effective product of inertia due to its large size and skewed mass distribution. Flowing down the requirement on the Spun Section Effective Product of Inertia to constraints on the mass properties of the RBA is important. The Spun Section is essentially comprised of three elements: the core structure with spin motor and feed assembly, the RBA, and a set of instrument electronics boxes. In configuring the Spun Section, the instrument electronics boxes are able to be placed nearly anywhere on the radial +X axis, from the spin axis out to the maximum

location where the boxes do not interfere with the payload fairing when in the launch configuration. With the flexibility of the instrument electronics boxes position plus the constraints, the Spun Section Effective Product of Inertia requirement can be flowed to two requirements controlling the mass properties of the RBA. These are the RBA Effective Product of Inertia and CMx constraint:

(1)

(2)

where mRBA is the mass of the RBA, xRBA and zRBA are the x and z center of mass locations of the RBA, and z0, C0, C1, and ε are constants. In these two constraints, the parameters C0, C1, and ε are determined by the mass properties and uncertainties associated with all the non-RBA spun hardware. Using these two requirements, RBA design can proceed with high confidence that a balanced Spun Section will result.

Figure 4 – Observatory Balancing

( ) ε≤−−+ 00 CzzxmI RBARBARBARBAxz

1Cxm RBARBA ≤

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Mass Uncertainty Analysis Model

Throughout the design process of the RBA, the Effective Product of Inertia and CMx constraints can be tracked to determine if the RBA meets the requirements. A finite element model is created in FEMAP to find the mass properties of the RBA and the constraints given in equations (1) and (2) can be calculated. When there is a design change, the mass properties model can be re-run to determine if the design change has a significant effect on the Effective Product of Inertia.

There are several uncertainties that contribute to the mass properties uncertainty of the RBA such as part mass, center of mass, position, moment of inertia, and product of inertia. A sensitivity study was performed to determine the major contributors to the mass properties uncertainty and it was found that part mass uncertainty was the significant source of overall RBA mass properties uncertainty. The part mass uncertainty is large due to the design maturity of the RBA. These large uncertainties are high in the beginning of the RBA design process and reduce as the design matures and is finalized.

Since there is a large variation in part mass during the RBA design process, a Monte Carlo simulation is set up to create random RBA mass configurations. For each configuration, the mass properties of the overall RBA system are found and the Effective Product of Inertia and CMx are calculated. The results are then analyzed to determine the number of cases that meet both requirements.

A FEMAP finite element model is used for the Monte Carlo simulation. Component mass values and the uncertainties are taken from a top level mass report which is a combination of measured mass values and CAD mass values. Random mass inputs are created in an Excel spreadsheet that uses a uniform distribution between the minimum and maximum mass of the parts. The finite element model uses 40 inputs for mass which is a combination of material densities and lumped masses.

A program is written with the FEMAP Application Programming Interface to input the random mass values from Excel to the FEMAP model, run mass properties within FEMAP, then export the mass properties back to Excel. The Monte Carlo simulation runs 5,000 random mass cases. Plots summarizing the Monte Carlo results for Effective Product of Inertia and CMx are shown in Figure 5. The plots show a histogram of the calculated Effective Product of Inertia and CMx for every case along with the limits of the constraints ε and C1.

Using the results from the Monte Carlo simulation, instant feedback can be obtained to determine if the current RBA design meets the Effective POI and CMx requirements.

Figure 5 - Plot of Monte Carlo Results for Effective POI and CMx

3. RBA MASS PROPERTY KNOWLEDGE Mass Knowledge Requirements

In order to balance the spun section to a near zero Effective Product of Inertia, the RBA has the capability to mount balance mass at the valley nodes around the reflector rim. Because of the size of the RBA, small amounts of balance mass are capable of large scale tuning of the spun section effective product of inertia. However, knowledge of the spun section mass properties is required in order to determine necessary balance mass quantities and locations.

The deployed RBA contributes significantly to the spun section product of inertia and center of mass. However, the deployed RBA mass properties are never measured in its deployed, as-spun state for the obvious reason that such a spin test would be nearly impossible to construct given the scale of the RBA, its flexibility, and the necessity to provide a vacuum and gravity offload during such a spin test.

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As a result, from a mass property knowledge standpoint the spun section is broken into two components: the RBA and the Spun Platform Assembly (SPA). The SPA is all the spun hardware that is not the RBA. The SPA can be spin balanced, resulting in precise knowledge of its center of mass position and product of inertias.

The SMAP Observatory has an allowable Spun Section Effective Product of Inertia determined by the wobble that the Observatory systems can tolerate. This is largely determined by allowable pointing error due to this effect and the allowable motion of the Observatory that the GNC sensors can tolerate. Given the allowable maximum Spun Section Effective Product of Inertia and the tolerances to which the SPA mass properties will be known as a result of the SPA spin balance, requirements on the mass property knowledge of the deployed, as-spun RBA can be derived.

The RBA mass property knowledge requirements require knowledge of 0.1 kg on the RBA mass, 10 mm on the RBA center of mass position, and 1.0 kg-m2 on the RBA Product of Inertias. Given these requirements, a mass property knowledge plan for the RBA has been developed which has the following four elements: 1) mass property measurements at the component and sub-assembly level, 2) selected mass property measurements at the boom and reflector level, 3) photogrammetry of the reflector and boom components to determine the positions of all the component hardware, and 4) analysis to determine the deployed RBA mass properties and errors on those mass properties. The process is refined such that the error determination falls within the mass property knowledge requirements.

Mass Property Knowledge Analysis Model

A finite element model is created using FEMAP to determine the RBA mass properties knowledge. The uncertainties considered in the analysis that contribute to the mass properties knowledge are:

1) Mass uncertainty – Accuracy of the scale when weighing the parts.

2) Part center of mass uncertainty – Error in the measurement of the center of mass for select critical components.

3) Part product of inertia uncertainty – Error added to select parts that are highly asymmetrical and critical to the overall product of inertia of the RBA.

4) Positional uncertainty – Error in the photogrammetry measurements to determine the position of the assembled components.

5) Dynamic distortion uncertainty – Error in stiffness measurements that are used to estimate the spin-deflected shape on orbit.

6) Part moisture loss uncertainty – Error in the part moisture loss tests. This data will be used to predict the reduction in mass of certain parts due to out-gassing on orbit

7) Thermal distortion uncertainty – Change in mass properties due to thermal distortions on orbit.

A sensitivity study is performed to examine the effects of the uncertainties on the RBA mass knowledge. Initially, assumptions are made for the scale accuracy used to weigh the parts and the part positional uncertainties. Using these uncertainties, worst case scenarios are created for the different mass properties to see if the worst cases exceed the budget of 1.0 kg-m2 for the product of inertias and 10 mm for the RBA center of mass.

It was found from the sensitivity study that the worst case for RBA product of inertia Izx exceeded the requirement; therefore a Monte Carlo simulation is set up to determine the mass properties knowledge. The Monte Carlo simulation involved running 10,000 cases using a uniform distribution of random inputs for the different mass uncertainties and center of mass/positional uncertainties. Uncertainty inputs are created in an Excel spreadsheet for each of the Monte Carlo cases. A program is created in FEMAP to input the uncertainty values from Excel, run mass properties on the system in FEMAP, and then extract the mass property values back to Excel where they can be evaluated. The random configurations are compared to the nominal configuration to obtain the mass knowledge.

The standard deviation σ of the mass properties is calculated from the Monte Carlo results and a 3σ value is used to determine the mass properties knowledge. Monte Carlo results for Izx product of inertia knowledge are shown in Table 1.

Table 1 – Izx Knowledge Monte Carlo Results

Izx Knowledge (kg-m2)

Std Dev Max Min +3σ -3σ

Truss Nodes 0.024 0.088 -0.083 0.07 -0.07Truss Tubes 0.005 0.015 -0.017 0.01 -0.01Front Net 0.008 0.023 -0.026 0.02 -0.02Rear Net 0.008 0.030 -0.034 0.03 -0.03Tension Ties 0.005 0.016 -0.017 0.02 -0.02Boom and PB 0.018 0.055 -0.060 0.05 -0.05

Total 0.20 -0.20

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From the sensitivity study, the required scale accuracy and accuracy of center of mass and positional measurements was found. Also, critical components were identified where the center of mass and inertia properties were significant to the overall system. For these components, the center of mass will be verified with a measurement. For all other components, the center of mass will be used from the CAD model. Additionally, it was found from the sensitivity study that the weight distribution knowledge of the Front and Rear Nets was critical to the overall mass properties and a more precise method of obtaining the weight of the nets needed to be considered.

A flow chart of the mass knowledge analysis process is shown in Figure 6. Initially, an unspun finite element model is created from the CAD mass, center of mass, and product and moment of inertias. The unspun finite element model is compared to the CAD model mass properties to verify that they match.

Once the unspun finite element model is verified with CAD, measured values can be used in the model. This includes mass measurements for every component and center of mass measurements for select critical components. Stiffness and moisture loss data is also taken into account in the finite element model. Photogrammetry is used to determine the position of components on the reflector and boom.

Using the measured values, a spin deflected finite element model can be created by applying the spin load and obtaining the deflected shape. A Monte Carlo simulation will then be performed on the spin deflected finite element model using uncertainty values obtained from the measurements to obtain the mass property knowledge values.

Analytical Method Verification

In order to verify the analytical method used to determine the mass properties knowledge of the RBA, the same process will be applied to the Prime Batten sub-assembly. The Prime Batten sub-assembly was chosen to validate the process because it is small enough that the MOI can be measured, yet still a complex component. The Prime Batten sub-assembly consists of the trapezoidal composite Prime Batten tube with bonded metallic fittings. The mass, center of mass, and MOI of the Prime Batten sub-assembly will be measured and will be compared to the finite element predictions.

4. RBA DEPLOYED FREQUENCY

Deployed Frequency Requirements

The SMAP Observatory has both an Attitude Control Subsystem and a Spin Subsystem that both contain controllers. Additionally, there is a clear disturbance source at the spin rate frequency and the first harmonic. Because of the controllers’ bandwidth and the disturbance sources, frequency separation is key for maintaining reliable and predictable Observatory performance, shown in Figure 7.

The RBA is the hardware element in the system that sets the first mode of the Observatory. As such, the first mode of the RBA in a configuration where it is attached to a spacecraft in a free-free state was required to be greater than 1.45 Hz, giving a decade separation between the Observatory first mode and bandwidth of the spin controller.

Additionally, based on system analysis the RBA is required to have a minimum of 0.2 Hz frequency separation between its first two modes. This is required to have the discrete

Figure 6 – Flow Chart for Mass Knowledge Analysis

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modes of RBA sufficiently separated in frequency such that they do not interact. Two low frequency modes close to each other in frequency may generate a much stronger pole frequency than the spin controller is designed for and hence break the margins of the spin controller.

Deployed Frequency Analysis Model

The deployed Astromesh reflector typically has three distinctive fixed based modes: yaw, pitch and roll, see Figure 8. The yaw mode is primarily torsion about the boom axis (Z), Figure 8(b). The pitch mode is boom bending about the Y axis, Figure 8(c). The roll mode is bending of the boom about the X axis, Figure 8(d). In addition to the boom stiffness, the interface between the reflector and the boom is critical for each mode. The yaw and pitch modes are often close while the roll mode is much larger.

The deployed frequency analysis for SMAP is unique since the first fixed base mode (yaw) is essentially motion about the spin axis. To create an effective set of deployed frequency requirements, the RBA is attached to a simplified mass representation of the spacecraft in a free-flying spacecraft configuration. The RBA is attached to the spun instrument (SPA) portion of the SMAP observatory represented by a rigid body which has the correct mass properties. The other component included in the model is the de-spun bus. In the finite element model, the RBA is rigidly attached to the SPA. The SPA is rigidly attached to the bus with the spin axis free to rotate. The mass properties of the SPA and of the bus each include a single lumped mass with representative inertia properties. In the resulting free-free deployed frequency analysis there are seven rigid body modes. The first 3 structural modes are: 1.8, 2.3, and 3.3 Hz as presented in Figures 9, 10, and 11. Note that the first mode is the Pitch Mode and the typical Yaw Mode is no longer the fundamental mode. Furthermore the simplified

Figure 7 – Key Frequency Separation

(a) Reflector FEM (b) Yaw Mode (d) Roll Mode(c) Pitch Mode

Figure 8 – Fixed Base Deployed Modes

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model of the spacecraft has been validated by attaching the RBA FEM to detail FEM of the spacecraft as shown in Figures 9, 10, and 11 and the resulting frequencies correlate well. Finally, the minimum frequency requirement and the frequency separation requirement between the first two modes have been met.

Figure 9 - First Free-Free Structural Mode, 1.8 Hz

Figure 10 - Second Free-Free Structural Mode, 2.3 Hz

Figure 11 - Third Free-Free Structural Mode, 3.3 Hz

Effect of Spin on Natural Frequency

It should be noted that the spun RBA will have higher frequencies compared to un-spun RBA [3]. However due to limitations of finite element software, the frequency requirements are based on a stationary or de-spun RBA configuration. Earlier in the project this effect was investigated using the ADAMS software. Astro Aerospace utilizes ADAMS software to determine the state of the reflector during its deployment. The natural frequency computation can be done indirectly inside ADAMS since it does have the Eigenvalue computation capability. The reflector in fully deployed configuration attached to a rigid stationary spacecraft (fixed base boundary condition) was given an external disturbance and from its steady state responses the natural frequency was determined. This process was done for both de-spun and at 14.6 RPM spun configurations. The results are presented in Table 2.

Table 2 – Comparison of Spun and Un-spun Natural

Frequency

Configuration Frequency Un-Spun 1.5 Hz, Pitch Mode Spinning at 14.6 RPM 1.63 Hz, Pitch Mode

5. RBA SURFACE ACCURACY Surface Accuracy Requirements

On orbit the RBA is subjected to thermal and to dynamic loading. The surface accuracy requirements are specified separately for constant and time varying errors. The constant error pointing requirement is ±100 millidegrees, while the time varying error is ±12 millidegrees. The time varying error is a combination of both diurnal and seasonal variations. The total surface error requirement is 2 mm, RMS of the half path length error (RMS hpl). The largest contributor to the constant pointing error is the centripetal acceleration of the nominal 14.6 rpm spin.

Surface Accuracy Analysis Model

The deployed RBA surface accuracy is analyzed using a finite element model. The analysis includes a Monte Carlo simulation to analyze the effects of manufacturing tolerances [4], on-orbit dynamics, and thermoelastic effects on the surface accuracy of the reflector. The thermoelastic analysis starts with thermal analysis to predict the member temperatures. The finite element model then uses these temperatures to predict the distortions. A typically thermoelastic distortion analysis was validated by test at JPL [5].

The location on the RBA furthest from the spin axis sees a 1.1 g acceleration due to the spin. The largest contributor to the diurnal variation is the thermal elastic distortions.

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For the SMAP program the mechanical pointing errors are multiplied by beam deviation factors (BDFs), which account for the difference between the mechanical pointing and the electrical pointing. The mechanical pointing error is the difference in position of the best fit paraboloid (BFP) and the design paraboloid. Pointing errors in this paper include BDFs of 1.83 (roll axis) and 1.65 (pitch axis).

To correct the spin induced constant pointing error the RBA is built such that it will deflect into the design position at the nominal 14.6 rpm spin rate. The change in pointing, from the as-built RBA to the nominal spin, is 350 millidegrees. The deflection at the reflector tip, furthest from the boom, is 2 cm. The built in correction accounts for the bending of the boom and for the flexibility at the boom/reflector interface. The relatively small distortions of the reflector truss and of the reflector surface are not accounted for in the as-built correction. The pointing error due to spin is corrected within the accuracy of the analysis and of the measurements. The analysis uncertainty and measurement uncertainties are budgeted in the constant pointing error. The residual surface error after the correction is made for the spin is 0.32 mm (RMS hpl). The maximum bow after correction in the truss is 1.7mm.

The reflector tension ties are designed to achieve an optimum tension field in the reflector webs while maintaining a minimum required tension in the webs to prevent web distortion and to react on orbit loading. For a typical Astromesh reflector the optimization is done without regard to external loading. For the SMAP reflector the optimization is done to include the loading due to the nominal spin. This allows for an optimum tension field at the nominal spin rate.

Additional constant error sources are measurement, zero-g effects, alignment, deployment repeatability, moisture release, web creep, and thermal bias. Pointing errors due to manufacturing will be eliminated during the reflector alignment. The current analysis predicts a total surface error of 1.6 mm (RMS hpl), and pointing errors 70 and 90 millidegrees about the roll and pitch axes.

The time varying pointing error is dominated by the thermal elastic distortion. The seasonal variation results in orbit beta angles from 58 to 89 degrees. The longest eclipse period occurs during the 58 degree orbit. The eclipse period is reduced with an increase in beta angle until 65 degrees is reached, at which the eclipse period is zero. The temperatures are calculated for the RBA components every two minutes for orbits of 58, 65, 78 and 89 degrees. The temperatures are mapped to the structural FEM, which is used to calculate the thermal elastic distortions. The pointing error for four orbits is shown in Figure 12. The BDF factor has been applied to the calculated mechanical point error. The resulting pointing error is a ±8 millidegrees with a thermal bias of 11 millidegrees. The thermal bias is a part of constant error budget and it could be corrected during the reflector build.

Figure 12 – Pointing Error

6. SUMMARY The SMAP instrument presents several design and analysis challenges due to the RBA rotating relative to the de-spun spacecraft. Among these challenges are the strict mass property control and knowledge requirements, natural frequency separation requirements, and surface accuracy requirements.

A Monte Carlo simulation is used for the mass property uncertainty analysis to determine the number of cases that meet the Effective POI and CMx mass property constraints. These constraints will be monitored throughout the design process/modifications to determine if the changes affect the overall system mass properties and a balanced system is maintained.

Due to the complexity of testing the product of inertia of the deployed reflector, the Monte Carlo simulation is used to show that the RBA meets the mass property knowledge requirement of 1.0 kg-m2 for product of inertia. The Monte Carlo simulation takes into account the different uncertainties such as mass and position. This analytical approach will be validated on the Prime Batten sub-assembly by measuring its mass, center of mass, and MOI and comparing to the predictions.

A deployed RBA finite element model that is attached to a simplified mass representation of a spacecraft is used for the frequency analysis. It is shown that the deployed model meets the minimum frequency requirements and the frequency separation requirement between the first two modes.

Monte Carlo analysis presented here shows that the deployed RBA will meet the surface accuracy and pointing error requirements. The uncertainties used in the Monte Carlo simulation include manufacturing tolerances, on-orbit dynamics, and thermoelastic effects. Also discussed is how the pointing error due to the on–orbit spin will be corrected

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for during the manufacturing of the RBA such that the RBA will deflect into the desired position at the nominal 14.6 rpm spin rate

ACKNOWLEDGEMENTS The research was carried out jointly by Astro Aerospace and the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

REFERENCES

[1] JPL SMAP Web site: http://smap.jpl.nasa.gov/

[2] M. Thomson, “Astromesh deployable reflectors for Ku- and Ka-band commercial satellites,” 20th AIAA International Communication Satellite Systems Conference and Exhibit, Montreal, Quebec, Canada, May 12-15, 2002

[3] L. Meirovitch, Computational Methods in Structural Dynamics, Sijthoff & Noordhoff International Publishers B.V., Alphen aan den Rijn, The Netherlands, 1980

[4] M. Mobrem, “Methods of analyzing surface accuracy of large antenna structures due to manufacturing tolerances,” 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia, April 7-10, 2003

[5] M.D. Stegman, M. Fedyk, and S. Kuehn, “Solar thermal vacuum testing of deployable mesh reflector for model correlation,” Aerospace Conference 2010 IEEE, Big Sky, Montana, March 6-13, 2010

BIOGRAPHIES

Mehran Mobrem received his B.S., M.S. and Ph.D. degrees from the University of California, Santa Barbara in Mechanical Engineering in 1977, 1980, and 1982, respectively. He is presently the head of the Analysis Department at NGAS Astro Aerospace. His areas of specialization are: large deployable structures, structural dynamics, structural optimization, and control systems. He joined Astro in 1978, and since then he has been involved in the design, analysis, and development of deployable structures and mechanisms on various programs for space applications. Dr. Mobrem has instructed numerous courses in the Design of Optimal Systems and Control Systems Design in the Mechanical Engineering Department at UCSB - 1982 to 1990.

Steve Kuehn has worked at NGAS Astro Aerospace since 1989 as a structural analyst. Starting in 1995, he has been involved in the development of the AstroMesh reflectors and in several AstroMesh flight programs. He obtained a BS in Mechanical Engineering from California Polytechnic State University, and an MS in Mechanical Engineering from Stanford University.

Chris Spier has been working at NGAS Astro Aerospace since 2010 as a structural analyst on the SMAP project. He received his PhD in 2007 in Mechanical Engineering, MS degree in 2005 in Mechanical Engineering, and BS degree in 2003 in Mechanical Engineering, all from the University of California, Santa Barbara.

Eric Slimko received his PhD from the California Institute of Technology in Computation and Neural Systems in 2006 and his Bachelors degree in Aerospace Engineering from the University of Michigan in 1994. He has been working at NASA’s Jet Propulsion Laboratory since 1990 on a wide range of flight projects and technology programs relevant to entry systems. He is currently the Instrument Mechanical System Engineer for the Soil Moisture Active & Passive Mission.