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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 253 records · Page 14

Hydrocarbon Cold-Flow Simulation of LOX/LH2 Rocket Aerodynamics

In FY19, this project developed a test method which employed heated ethane in the physical simulation of rocket plume aerodynamics. Based on this work, EUS partnered with significant leveraged funding. A portable, self-contained test bed was also fabricated to support validation of the new method. In FY20, this project focused on the formal validation of ethane’s performance as an aerodynamic simulant as well as the development of the analytical and hardware infrastructure required to carry out that task. The test bed was activated, a series of heated-ethane tests on one or more rocket/diffuser configurations were conducted, and characterizations of the performance of the ethane simulation compared to hot-fire were performed. A series of 127 tests were conducted on 13 aerodynamic configurations to evaluate ethane’s performance as a simulant. It was found that the new methodology can reproduce rocket plume flow fields with +/- 0.5% pressure error at ~3% physical scale. The result is a cost-per-test reduction of ~99% compared to the hot-fire subscale testing typically used to obtain equivalent data. Some initial efforts have taken place, and future efforts are being planned with LaRC supersonic retro propulsion and MSFC SLS aerodynamics teams, which are interested in using the ethane system to wind-tunnel test human-rated Mars lander retrorockets and SLS Booster. Details of the prototypical experiments were published as NASA TM 2020-5009122,and have been presented in JANNAF Virtual Conference paper, "New Developments in Retro propulsion Testing for Mars Entry, Descent and Landing".

Daniel Jones↗

NASA CEV On-Orbit GN&C Analysis

The Orion spacecraft orbit GN&C system will be required to perform both ISS servicing missions and Lunar sortie and outpost crew transportation. While certain aspects of these two missions are complementary, the two missions are also distinct in many ways. Common between the missions is a Low Earth Orbit (LEO) rendezvous, one with the ISS And the other with the LSAM/EDS stack prior to trans-lunar insertion. The lunar missions will additionally require Orion to perform orbit maintenance in LLO, perform contingency lunar orbit operations including RPOD with the LSAM, perform the TEI maneuver sequence, and execute the trans-Earth cruise. The NASA-led team developed a reference configuration orbit GN&C system capable of executing all of these activities with the same navigation sensor suite and control effectors while fully meeting the requirements being developed for System Requirements Review in advance of prime contractor selection. This paper will present an overview of the analyses performed to support system trade studies, demonstrate the feasibility of the NASA reference configuration, and validate the Orion system requirements. These analyses include linear covariance techniques, 3-DOF Monte Carlo simulations, 6-DOF Monte Carlo simulations, and analytical evaluations of GN&C systems performed by the NASA-led Orion team to characterize the sensitivities of Orion s various missions and assess the unique challenges of each. The first part of this paper will describe the trade studies that were performed in order to characterize the RPOD system performance for both the ISS and the lunar missions including development of an RPOD operations concept, RPOD trajectories, contingency scenarios, docking mechanism and associated contact conditions, post-contact thrust issues, relative navigation sensors, relative navigation sensor target infrastructure. The paper will also discuss concepts for both manually-piloted and automatically executed scenarios, as well as the remotely-piloted contingency scenario in LLO. The second part of the paper will discuss the analyses performed for lunar and cislunar GN&C performance including the accuracy of the post-insertion lunar orbit, the ability of Orion to hit a particular Earth return entry corridor, attitude control solutions for long-duration surface operations, and autonomous navigation in support of TEI without ground tracking.

DSouza, Chris↗

Development and use of computational techniques in Army Aviation research and development programs for crash resistant helicopter technology

During the 1960's over 30 full-scale aircraft crash tests were conducted by the Flight Safety Foundation under contract to the Aviation Applied Technology Directorate (AATD) of the U.S. Army Aviation Systems Command (AVSCOM). The purpose of these tests were to conduct crash injury investigations that would provide a basis for the formulation of sound crash resistance design criteria for light fixed-wing and rotary wing aircraft. This resulted in the Crash Survival Design Criteria Designer's Guide which was first published in 1967 and has been revised numerous times, the last being in 1989. Full-scale aircraft crash testing is an expensive way to investigate structural deformations of occupied spaces and to determine the decelerative loadings experienced by occupants in a crash. This gave initial impetus to the U.S. Army to develop analytical methods to predict the dynamic response of aircraft structures in a crash. It was believed that such analytical tools could be very useful in the preliminary design stage of a new helicopter system which is required to demonstrate a level of crash resistance and had to be more cost effective than full-scale crash tests or numerous component design support tests. From an economic point of view, it is more efficient to optimize for the incorporation of crash resistance features early in the design stage. However, during preliminary design it is doubtful if sufficient design details, which influence the exact plastic deformation shape of structural elements, will be available. The availability of simple procedures to predict energy absorption and load-deformation characteristics will allow the designer to initiate valuable cost, weight, and geometry tradeoff studies. The development of these procedures will require some testing of typical specimens. This testing should, as a minimum, verify the validity of proposed procedures for providing pertinent nonlinear load-deformation data. It was hoped that through the use of these analytical models, the designer could optimize aircraft design for crash resistance from both a weight and cost increment standpoint, thus enhancing the acceptance of the design criteria for crash resistance.

Burrows, Leroy T.↗

Design Considerations of ISTAR Hydrocarbon Fueled Combustor Operating in Air Augmented Rocket, Ramjet and Scramjet Modes

The development and ground test of a rocket-based combined cycle (RBCC) propulsion system is being conducted as part of the NASA Marshall Space Flight Center (MSFC) Integrated System Test of an Airbreathing Rocket (ISTAR) program. The eventual flight vehicle (X-43B) is designed to support an air-launched self-powered Mach 0.7 to 7.0 demonstration of an RBCC engine through all of its airbreathing propulsion modes - air augmented rocket (AAR), ramjet (RJ), and scramjet (SJ). Through the use of analytical tools, numerical simulations, and experimental tests the ISTAR program is developing and validating a hydrocarbon-fueled RBCC combustor design methodology. This methodology will then be used to design an integrated RBCC propulsion system that produces robust ignition and combustion stability characteristics while maximizing combustion efficiency and minimizing drag losses. First order analytical and numerical methods used to design hydrocarbon-fueled combustors are discussed with emphasis on the methods and determination of requirements necessary to establish engine operability and performance characteristics.

Andreadis, Dean↗

Design Considerations of Istar Hydrocarbon Fueled Combustor Operating in Air Augmented Rocket, Ramjet and Scramjet Modes

The development and ground test of a rocket-based combined cycle (RBCC) propulsion system is being conducted as part of the NASA Marshall Space Flight Center (MSFC) Integrated System Test of an Airbreathing Rocket (ISTAR) program. The eventual flight vehicle (X-43B) is designed to support an air-launched self-powered Mach 0.7 to 7.0 demonstration of an RBCC engine through all of its airbreathing propulsion modes - air augmented rocket (AAR), ramjet (RJ), and scramjet (SJ). Through the use of analytical tools, numerical simulations, and experimental tests the ISTAR program is developing and validating a hydrocarbon-fueled RBCC combustor design methodology. This methodology will then be used to design an integrated RBCC propulsion system thai: produces robust ignition and combustion stability characteristics while maximizing combustion efficiency and minimizing drag losses. First order analytical and numerical methods used to design hydrocarbon-fueled combustors are discussed with emphasis on the methods and determination of requirements necessary to establish engine operability and performance characteristics.

Andreadis, Dean↗

Study of a 30-M Boom For Solar Sail-Craft: Model Extendibility and Control Strategy

Space travel propelled by solar sails is motivated by the fact that the momentum exchange that occurs when photons are reflected and/or absorbed by a large solar sail generates a small but constant acceleration. This acceleration can induce a constant thrust in very large sails that is sufficient to maintain a polar observing satellite in a constant position relative to the Sun or Earth. For long distance propulsion, square sails (with side length greater than 150 meters) can reach Jupiter in two years and Pluto in less than ten years. Converting such design concepts to real-world systems will require accurate analytical models and model parameters. This requires extensive structural dynamics tests. However, the low mass and high flexibility of large and light weight structures such as solar sails makes them unsuitable for ground testing. As a result, validating analytical models is an extremely difficult problem. On the other hand, a fundamental question can be asked. That is whether an analytical model that represents a small-scale version of a solar-sail boom can be extended to much larger versions of the same boom. To answer this question, we considered a long deployable boom that will be used to support the solar sails of the sail-craft. The length of fully deployed booms of the actual solar sail-craft will exceed 100 meters. However, the test-bed we used in our study is a 30 meter retractable boom at MSFC. We first develop analytical models based on Lagrange s equations and the standard Euler-Bernoulli beam. Then the response of the models will be compared with test data of the 30 meter boom at various deployed lengths. For this stage of study, our analysis was limited to experimental data obtained at 12ft and 18ft deployment lengths. The comparison results are positive but speculative. To observe properly validate the analytic model, experiments at longer deployment lengths, up to the full 30 meter, have been requested. We expect the study to answer the extendibility question of the analytical models. In operation, rapid temperature changes can be induced in solar sails as they transition from day to night and vice versa. This generates time dependent thermally induced forces, which may in turn create oscillation in structural members such as booms. Such oscillations have an adverse effect on system operations, precise pointing of instruments and antennas and can lead to self excited vibrations of increasing amplitude. The latter phenomenon is known as thermal flutter and can lead to the catastrophic failure of structural systems. To remedy this problem, an active vibration suppression system has been developed. It was shown that piezoelectric actuators used in conjunction with a Proportional Feedback Control (PFC) law (or Velocity Feedback Control (VFC) law) can induce moments that can suppress structural vibrations and prevent flutter instability in spacecraft booms. In this study, we will investigate control strategies using piezoelectric transducers in active, passive, and/or hybrid control configurations. Advantages and disadvantages of each configuration will be studied and experiments to determine their capabilities and limitations will be planned. In particular, special attention will be given to the hybrid control, also known as energy recycling, configuration due to its unique characteristics.

Keel, Leehyun↗

Large deflection random response of a pipe containing fluid flow subjected to random loading

An analytic approach is developed for beam type pipes undergoing large deflections subjected to random loadings. The influence of fluid velocity on the random response is investigated. The root-mean-square (rms) deflections and frequencies for different sound spectrum level values are determined for pipes with both ends either simply supported or clamped. The required number of modes to achieve accurate rms deflections and strains is also studied. The prediction of fatigue life is then based on obtained rms maximum stress. This analytical investigation will help to broaden the basic understanding of the role of fluid flow within structures subjected to acoustic loading.

Chiang, C. K.↗

TBCC Discipline Overview. Hypersonics Project

The "National Aeronautics Research and Development Policy" document, issued by the National Science and Technology Council in December 2006, stated that one (among several) of the guiding objectives of the federal aeronautics research and development endeavors shall be stable and long-term foundational research efforts. Nearly concurrently, the National Academies issued a more technically focused aeronautics blueprint, entitled: the "Decadal Survey of Civil Aeronautics - Foundations for the Future." Taken together these documents outline the principles of an aeronautics maturation plan. Thus, in response to these overarching inputs (and others), the National Aeronautics and Space Administration (NASA) organized the Fundamental Aeronautics Program (FAP), a program within the NASA Aeronautics Research Mission Directorate (ARMD). The FAP initiated foundational research and technology development tasks to enable the capability of future vehicles that operate across a broad range of Mach numbers, inclusive of the subsonic, supersonic, and hypersonic flight regimes. The FAP Hypersonics Project concentrates on two hypersonic missions: (1) Air-breathing Access to Space (AAS) and (2) the (Planetary Atmospheric) Entry, Decent, and Landing (EDL). The AAS mission focuses on Two-Stage-To-Orbit (TSTO) systems using air-breathing combined-cycle-engine propulsion; whereas, the EDL mission focuses on the challenges associated with delivering large payloads to (and from) Mars. So, the FAP Hypersonic Project investments are aligned to achieve mastery and intellectual stewardship of the core competencies in the hypersonic-flight regime, which ultimately will be required for practical systems with highly integrated aerodynamic/vehicle and propulsion/engine technologies. Within the FAP Hypersonics, the technology management is further divided into disciplines including one targeting Turbine-Based Combine-Cycle (TBCC) propulsion. Additionally, to obtain expertise and support from outside (including industry and academia) the hypersonic uses both NASA Research Announcements (NRAs) and a jointly sponsored, Air Force Office of Scientific Research and NASA, National Hypersonic Science Center that are focused on propulsion research. Finally, these two disciplines use selected external partnership agreements with both governmental agencies and industrial entities. The TBCC discipline is comprised of analytic and experimental tasks, and is structured into the following two research topic areas: (1) TBCC Integrated Flowpath Technologies, and (2) TBCC Component Technologies. These tasks will provide experimental data to support design and analysis tool development and validation that will enable advances in TBCC technology.

Thomas, Scott R.↗

Rotorcraft Optimization Tools: Incorporating Rotorcraft Design Codes into Multi-Disciplinary Design, Analysis, and Optimization

One of the goals of NASA's Revolutionary Vertical Lift Technology Project (RVLT) is to provide validated tools for multidisciplinary design, analysis and optimization (MDAO) of vertical lift vehicles. As part of this effort, the software package, RotorCraft Optimization Tools (RCOTOOLS), is being developed to facilitate incorporating key rotorcraft conceptual design codes into optimizations using the OpenMDAO multi-disciplinary optimization framework written in Python. RCOTOOLS, also written in Python, currently supports the incorporation of the NASA Design and Analysis of RotorCraft (NDARC) vehicle sizing tool and the Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics II (CAMRAD II) analysis tool into OpenMDAO-driven optimizations. Both of these tools use detailed, file-based inputs and outputs, so RCOTOOLS provides software wrappers to update input files with new design variable values, execute these codes and then extract specific response variable values from the file outputs. These wrappers are designed to be flexible and easy to use. RCOTOOLS also provides several utilities to aid in optimization model development, including Graphical User Interface (GUI) tools for browsing input and output files in order to identify text strings that are used to identify specific variables as optimization input and response variables. This paper provides an overview of RCOTOOLS and its use

Analysi↗

Dynamic Impact Testing and Model Development in Support of NASA's Advanced Composites Program

The purpose of this presntation is to provide an executive overview of the HEDI effort for NASAs Advanced Composites Program and establish the foundation for the remaining papers to follow in the 2018 SciTech special session NASA ACC High Energy Dynamic Impact. The paper summarizes the work done for the Advanced Composites Program to advance our understanding of the behavior of composite materials during high energy impact events and to advance the ability of analytical tools to provide predictive simulations. The experimental program carried out at GRC is summarized and a status on the current development state for MAT213 will be provided. Future work will be discussed as the HEDI effort transitions from fundamental analysis and testing to investigating sub-component structural concept response to impact events.

Melis, Matthew E.↗

Dynamic Impact Testing and Model Development in Support of NASA's Advanced Composites Program

The purpose of this paper is to provide an executive overview of the HEDI effort for NASA's Advanced Composites Program and establish the foundation for the remaining papers to follow in the 2018 SciTech special session NASA ACC High Energy Dynamic Impact. The paper summarizes the work done for the Advanced Composites Program to advance our understanding of the behavior of composite materials during high energy impact events and to advance the ability of analytical tools to provide predictive simulations. The experimental program carried out at GRC is summarized and a status on the current development state for MAT213 will be provided. Future work will be discussed as the HEDI effort transitions from fundamental analysis and testing to investigating sub-component structural concept response to impact events.

Melis, Matthew E.↗

Control and dynamics of an anti-friction levitation system

A novel anti-friction levitator concept has been devised and analytically evaluated to overcome support bearing friction and thereby minimize the structural damping of the Large Spacecraft Control Laboratory (LSCL) experiment structure at JPL. A dynamic model and controller design have been developed for the new levitation system. Simulation results show excellent system performance even when the system is subjected to significant measurement noise and hardware saturation effects.

Ih, C.-H. C.↗

AC and DC Fault Management for Megawatt Electrified Aircraft Electrical Powertrains Task 3: Lifetime and Reliability of Electrical Insulators

This research project was a collaborative investigation between researchers at the RTX Technology Research Center (RTRC) and the University of Texas at Austin and made a significant contribution to enabling electric aircraft. The transport of electric power between the points of generation and use requires power cables. These cables must be smaller, lighter and provide a more predictable life than power cables used in stationary applications. Consequently, this investigation provided heretofore unavailable information supporting the safety and reliability of smaller lighter power cables for electrified aircraft. In addition, the research identified key additional engineering data needed to support quantitative reliability assessments. Important advances included: • Demonstrated that at least one manufacturer can make a novel, smaller, lighter power cable that is free from serious defects. • Developed and published an appropriate analytical construct to describe the life of this novel cable. This is a necessary step for use in aviation where the understanding of remaining life is critical. • Demonstrated thermal-mechanical aging that suggested 1000+ flights before the thermal-mechanical processes produced defects large enough that the defect growth was accelerated electrically. • Showed that electrical aging took place at two rates. The first possibly lasting weeks to months and the second possibly days to weeks. If robust, this provides a good diagnostic for cable replacement. • Demonstrated that the traditional electrical testing of cable materials using manufactured voids can be misleading due to the size of the voids. Emerging laser drilling technology permitted demonstration that the physics of failure in realistically small voids is different from that in the unrealistically large voids used in earlier research, which is very important for high-quality, high-performance, small aircraft cables. Although this project represents a significant contribution to the specifics of cable aging in the aircraft environment, important additional research remains to be completed, including: • Non-uniform thermal cycling by applying the heat from the center conductor to maximize thermal stress next to the core area where the electric gradient is the strongest. This builds on the uniform thermal cycling that has been completed. • The augmentation of the thermal-mechanical failure rate by electrical processes. Better understanding of these time constants strongly affects the ability to predict life. • Termination design: Terminations provide not only electrical reflection potential, but a location for a series arc fault and an area where ozone can diffuse into the center conductor and negatively affect cable insulation. • The abrasion and ozone resistance of the cable jacket. • Pressure cycling as an accelerant of thermal, mechanical, and/or electrical aging. • Possible methods for online PD detection and offline PD localization

model↗

Helical Face Gear Development Under the Enhanced Rotorcraft Drive System Program

U.S. Army goals for the Enhanced Rotorcraft Drive System Program are to achieve a 40 percent increase in horsepower to weight ratio, a 15 dB reduction in drive system generated noise, 30 percent reduction in drive system operating, support, and acquisition cost, and 75 percent automatic detection of critical mechanical component failures. Boeing s technology transition goals are that the operational endurance level of the helical face gearing and related split-torque designs be validated to a TRL 6, and that analytical and manufacturing tools be validated. Helical face gear technology is being developed in this project to augment, and transition into, a Boeing AH-64 Block III split-torque face gear main transmission stage, to yield increased power density and reduced noise. To date, helical face gear grinding development on Northstar s new face gear grinding machine and pattern-development tests at the NASA Glenn/U.S. Army Research Laboratory have been completed and are described.

Heath, Gregory F.↗

Reference manual for the Thermal Analyst's Help Desk Expert System

This document provides technical information and programming guidance for the maintenance and future development of the Thermal Analyst's Help Desk. Help Desk is an expert system that operates within the EXSYSTM expert system shell, and is used to determine first approximations of thermal capacity for spacecraft and instruments. The five analyses supported in Help Desk are: (1) surface area required for a radiating surface, (2) equilibrium temperature of a surface, (3) enclosure temperature and heat loads for a defined position in orbit, (4) enclosure temperature and heat loads over a complete orbit and, (5) selection of appropriate surface properties. The two geometries supported by Help Desk are a single flat plate and a rectangular box enclosure. The technical information includes the mathematical approach and analytical derivations used in the analyses such as: radiation heat balance, view factor calculation, and orbit determination with coordinate transformation. The programming guide for developers describes techniques for enhancement of Help Desk. Examples are provided showing the addition of new features, user interface development and enhancement, and external program interfaces.

Ormsby, Rachel A.↗

Spaceliner Class Operability Gains Via Combined Airbreathing/ Rocket Propulsion: Summarizing an Operational Assessment of Highly Reusable Space Transports

In discussing a new NASA initiative in advanced space transportation systems and technologies, the Director of the NASA Marshall Space Flight Center, Arthur G. Stephenson, noted that, "It would use new propulsion technology, air-breathing engine so you don't have to carry liquid oxygen, at least while your flying through the atmosphere. We are calling it Spaceliner 100 because it would be 100 times cheaper, costing $ 100 dollars a pound to orbit." While airbreathing propulsion is directly named, rocket propulsion is also implied by, "... while you are flying through the atmosphere." In-space final acceleration to orbital speed mandates rocket capabilities. Thus, in this informed view, Spaceliner 100 will be predicated on combined airbreathing/rocket propulsion, the technical subject of this paper. Interestingly, NASA's recently concluded Highly Reusable Space Transportation (HRST) study focused on the same affordability goal as that of the Spaceliner 100 initiative and reflected the decisive contribution of combined propulsion as a way of expanding operability and increasing the design robustness of future space transports, toward "aircraft like" capabilities. The HRST study built on the Access to Space Study and the Reusable Launch Vehicle (RLV) development activities to identify and characterize space transportation concepts, infrastructure and technologies that have the greatest potential for reducing delivery cost by another order of magnitude, from $1,000 to $100-$200 per pound for 20,000 lb. - 40.000 lb. payloads to low earth orbit (LEO). The HRST study investigated a number of near-term, far-term, and very far-term launch vehicle concepts including all-rocket single-stage-to-orbit (SSTO) concepts, two-stage-to-orbit (TSTO) concepts, concepts with launch assist, rocket-based combined cycle (RBCC) concepts, advanced expendable vehicles, and more far term ground-based laser powered launchers. The HRST study consisted of preliminary concept studies, assessments and analysis tool development for advanced space transportation systems, followed by end-to-end system concept definitions and trade analyses, specific system concept definition and analysis, specific key technology and topic analysis, system, operational and economics model development, analysis, and integrated assessments. The HRST Integration Task Force (HITF) was formed to synthesize study results in several specific topic areas and support the development of conclusions from the study: Systems Concepts Definitions, Technology Assessment, Operations Assessment, and Cost Assessment. This paper summarizes the work of the Operations Assessment Team: the six approaches used, the analytical tools and methodologies developed and employed, the issues and concerns, and the results of the assessment. The approaches were deliberately varied in measures of merit and procedure to compensate for the uncertainty inherent in operations data in this early phase of concept exploration. In general, rocket based combined cycle (RBCC) concepts appear to have significantly greater potential than all-rocket concepts for reducing operations costs.

Nix, Michael B.↗

Digital Image Correlation Techniques Applied to Large Scale Rocket Engine Testing

Rocket engine hot-fire ground testing is necessary to understand component performance, reliability and engine system interactions during development. The J-2X upper stage engine completed a series of developmental hot-fire tests that derived performance of the engine and components, validated analytical models and provided the necessary data to identify where design changes, process improvements and technology development were needed. The J-2X development engines were heavily instrumented to provide the data necessary to support these activities which enabled the team to investigate any anomalies experienced during the test program. This paper describes the development of an optical digital image correlation technique to augment the data provided by traditional strain gauges which are prone to debonding at elevated temperatures and limited to localized measurements. The feasibility of this optical measurement system was demonstrated during full scale hot-fire testing of J-2X, during which a digital image correlation system, incorporating a pair of high speed cameras to measure three-dimensional, real-time displacements and strains was installed and operated under the extreme environments present on the test stand. The camera and facility setup, pre-test calibrations, data collection, hot-fire test data collection and post-test analysis and results are presented in this paper.

Gradl, Paul R.↗

Suspension systems for ground testing large space structures

A research program is documented for the development of improved suspension techniques for ground vibration testing of large, flexible space structures. The suspension system must support the weight of the structure and simultaneously allow simulation of the unconstrained rigid-body movement as in the space environment. Exploratory analytical and experimental studies were conducted for suspension systems designed to provide minimum vertical, horizontal, and rotational degrees of freedom. The effects of active feedback control added to the passive system were also investigated. An experimental suspension apparatus was designed, fabricated, and tested. This test apparatus included a zero spring rate mechanism (ZSRM) designed to support a range of weights from 50 to 300 lbs and provide vertical suspension mode frequencies less than 0.1 Hz. The lateral suspension consisted of a pendulum suspended from a moving cart (linear bearing) which served to increase the effective length of the pendulum. The torsion suspension concept involved dual pendulum cables attached from above to a pivoting support (bicycle wheel). A simple test structure having variable weight and stiffness characteristics was used to simulate the vibration characteristics of a large space structure. The suspension hardware for the individual degrees of freedom was analyzed and tested separately and then combined to achieve a 3 degree of freedom suspension system. Results from the exploratory studies should provide useful guidelines for the development of future suspension systems for ground vibration testing of large space structures.

Gold, Ronald R.↗