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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 73 records · Page 4

Preliminary Plan to Inform Testing of a Heat Exchanger Test Article

This report presents a preliminary plan to guide the qualification testing of advanced heat exchanger (HX) components for nuclear-to-industrial heat transfer applications. The objective is to establish a defensible, physics-based methodology that integrates computational modeling, targeted experimentation, and in-service inspection considerations to demonstrate component performance and reliability under representative reactor conditions. The analysis identifies Sodium-cooled Fast Reactor (SFR) and High-Temperature Gas-cooled Reactor (HTGR) systems as reference configurations in terms of temperature, pressure, and chemical environment. Within these operating envelopes, dominant degradation mechanisms— including creep–fatigue interaction, flow-induced vibration, corrosion, and diffusion-bond deterioration—were evaluated to define test requirements. A comprehensive computationalexperimental framework is proposed to support life prediction and qualification activities. The framework couples high-fidelity structural-mechanics, thermal-hydraulic, and fluid-structure interaction models with accelerated degradation testing to produce a traceable linkage between microstructural evolution, mechanical performance, and remaining useful life (RUL). The approach adheres to established Verification, Validation, and Uncertainty Quantification (VVUQ) standards (ASME V&V 10/20; NUREG-2152) and incorporates a digital-twin architecture for continuous model refinement through data assimilation. The plan further outlines testing methodologies, including pre-test analyses, test-loop design parameters, and sensor placement strategies that maximize information yield while maintaining mechanistic fidelity. Complementary sections describe in-service inspection (ISI), on-line monitoring (OLM), and structural-health-monitoring (SHM) techniques applicable to compact HX geometries typical of advanced reactors. Collectively, these activities establish the technical foundation for demonstrating 40-60-year equivalent service life of advanced heat exchangers in support of the U.S. Department of Energy’s Advanced Reactor and Integrated Energy Systems programs. The forthcoming phase will execute the defined pre-test analyses, initiate hardware fabrication, and implement the integrated testing campaign to validate the proposed qualification methodology.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Improvement in the control aspect of laser frequency stabilization for SUNLITE project

Flight Electronics Division of Langley Research Center is developing a spaceflight experiment called the Stanford University and NASA Laser In-Space Technology (SUNLITE). The objective of the project is to explore the fundamental limits on frequency stability using an FM laser locking technique on a Nd:YAG non-planar ring (free-running linewidth of 5 KHz) oscillator in the vibration free, microgravity environment of space. Compact and automated actively stabilized terahertz laser oscillators will operate in space with an expected linewidth of less than 3 Hz. To implement and verify this experiment, NASA engineers have designed and built a state of the art, space qualified high speed data acquisition system for measuring the linewidth and stability limits of a laser oscillator. In order to achieve greater stability and better performance, an active frequency control scheme requiring the use of a feedback control loop has been applied. In the summer of 1991, the application of control theory in active frequency control as a frequency stabilization technique was investigated. The results and findings were presented in 1992 at the American Control Conference in Chicago, and have been published in Conference Proceedings. The main focus was to seek further improvement in the overall performance of the system by replacing the analogue controller by a digital algorithm.

Zia, Omar↗

A Risk Analysis Tool for Estimating the Risk of Electrical Failures Due to Human Induced Defects

Aerospace electrical systems are required to withstand and adequately operate in extremely harsh environments that include, for example, high radiation exposure, temperature extremes, intense vibrational stress and drastic temperature cycling. The nature of aerospace electronics also demands high reliability since, with very few exceptions, there is no chance for hardware servicing or repairs. Common risk mitigation techniques for this type of situation are to perform a Reliability Analysis of the system throughout the development cycle, and to use electrical components that are regarded as “high reliability” because of additional controls and requirements applied in their design, manufacturing and testing. Unfortunately, studies have shown that even though these techniques are used, many systems fail to meet mission requirements well before the predicted lifetimes. This paper presents the analysis of failures of electrical parts, experienced during various stages of system development, at NASA Goddard Space Flight Center, Greenbelt MD, between the years 2001 and 2013. These components were subjected to qualification, screening and testing in which the goal was to ensure that the components would survive the stresses of the mission. The analysis categorizes failures by part type and failure mechanisms. One of the results of the analysis was the realization that a surprising proportion of failures experienced during system integration and testing were caused by human error (i.e. human induced defect). Further analysis included the determination of root failure mechanisms and any influencing factors contributing to these failures. The major causes of these defects were attributed to electrostatic damage (ESD), electrical overstress (EOS), mechanical overstress (MOS), and thermal overstress (TOS). Finally, the study proposes a risk analysis tool which incorporates these major causes for the failures, termed error-producing conditions (EPCs), and a proportionality factor representing the number of each type of failure that has occurred at the facility under study. These factors are quantified and used to communicate the risk of human induced defects for the assembly, integration and testing of space hardware based on the system’s electrical parts list. The new risk identification can trigger risk-mitigating actions more effectively, based on the presence of component categories or other hazardous conditions that have a history of failure due to human error.

Majewicz, Peter J.↗

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Thermal Expansion (DTE) Thermal Switch (TS) for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the TS operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center (MSFC) including the vibration (vibe) test, pre-vibe thermal vacuum (t-vac) cycle test, post-vibe t-vac cycle test, and long duration t-vac cycle test. The data collected from the pre- and post-vibe tests are compared to show the impact of the vibe test on performance. The data collected from the long duration test is used to calculate the total thermal contact conductance through the TS interfaces for both ‘on’ (TS closed, during hot plateau) and ‘off’ (TS open, during cold plateau) configurations, and the turndown ratio is also calculated. Challenges experienced throughout testing are also discussed.

Thermal control technology↗

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Thermal Expansion (DTE) Thermal Switch (TS) for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the TS operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center (MSFC) including the vibration (vibe) test, pre-vibe thermal vacuum (t-vac) cycle test, post-vibe t-vac cycle test, and long duration t-vac cycle test. The data collected from the pre- and post-vibe tests are compared to show the impact of the vibe test on performance. The data collected from the long duration test is used to calculate the total thermal contact conductance through the TS interfaces for both ‘on’ (TS closed, during hot plateau) and ‘off’ (TS open, during cold plateau) configurations, and the turndown ratio is also calculated. Challenges experienced throughout testing are also discussed.

Thermal control technology↗

Signal Processing Methods for Removing the Effects of Whole Body Vibration upon Speech

Humans may be exposed to whole-body vibration in environments where clear speech communications are crucial, particularly during the launch phases of space flight and in high-performance aircraft. Prior research has shown that high levels of vibration cause a decrease in speech intelligibility. However, the effects of whole-body vibration upon speech are not well understood, and no attempt has been made to restore speech distorted by whole-body vibration. In this paper, a model for speech under whole-body vibration is proposed and a method to remove its effect is described. The method described reduces the perceptual effects of vibration, yields higher ASR accuracy scores, and may significantly improve intelligibility. Possible applications include incorporation within communication systems to improve radio-communication systems in environments such a spaceflight, aviation, or off-road vehicle operations.

human response to vibration↗

Modal Analysis and Testing of a Cantilever Beam: Results and Guide

This report discusses modal analysis and testing of a cantilever beam including an introduction to modal testing, simulation, analysis, and a comparison of results. An accompanying presentation can be found from the LLNL CASIS website. Modal testing and analysis are essential for characterizing the response of a structure during vibration environments. Determining natural frequencies and mode shapes helps determine whether resonances will be reached during operations and if so, how the structure will respond and how the response can be tuned. The goal of this work is to convey the basics of modal testing and analysis through a simple project. This can be applied later to more complex, applicable structures. This includes a variety of work including data collection, finite element analysis and data processing. For this project a cantilever beam was chosen because it is a simple, well-characterized structure.

42 ENGINEERING↗

Flight set 360L003 instrumentation final test report, volume 9

Post-flight instrumentation hardware and data evaluation for 360L003 is summarized. The 360L003 motors were equipped with Developmental Flight Instrumentation (DFI), Operational Flight Instrumentation (OFI), and Ground Environmental Instrumentation (GEI). The DFI was designed to measure strain, temperature, pressure, and vibration at various locations on the motor during flight. The DFI is used to validate engineering models in a flight environment. The OFI consists of six Operational Pressure Tranducers which monitor chamber pressure during flight. These pressure transducers are used in the SRB separation cue. GEI measures the motor case, igniter flange, and nozzle temperature prior to launch.

Source record↗

Assessment of Stirling Technology Has Provided Critical Data Leading Toward Flight Readiness of the Stirling Converter

The NASA Glenn Research Center is supporting the development of a Stirling converter with the Department of Energy (DOE, Germantown, Maryland) for an advanced Stirling Radioisotope Power System (SRPS) to provide spacecraft onboard electric power for NASA space science missions. A key technology assessment completed by Glenn and DOE has led to the SRPS being identified as a high-efficiency power source for such deep space missions as the Europa Orbiter and the Solar Probe. In addition, the Stirling system is now being considered for unmanned Mars rovers, especially where mission profiles may exclude the use of photovoltaic power systems, such as exploration at high Martian latitudes or for missions of long duration. The SRPS efficiency of over 20 percent will reduce the required amount of radioisotope by more than a factor of 3 in comparison to current radioisotope thermoelectric generators. This significantly reduces radioisotope cost, radiological inventory, and system cost, and it provides efficient use of scarce radioisotope resources. In support of this technology assessment, Glenn conducted a series of independent evaluations and tests to determine the technology readiness of a 55-We Stirling converter developed by Stirling Technology Company (Kennewick, Washington) and DOE. Key areas evaluated by Glenn included: 1) Radiation tolerance of materials; 2) Random vibration testing of the Stirling converter in Glenn's Structural Dynamics Lab to simulate operation in the launch environment; 3) Electromagnetic interference and compatibility (EMI/EMC) of the converter operating in Glenn's EMI lab; Independent failure modes, effects, and criticality analysis, and life and reliability 4. Independent failure modes, effects, and criticality analysis, and life and reliability assessment; and 5) SRPS cost estimate. The data from these evaluations were presented to NASA Headquarters and the Jet Propulsion Laboratory mission office by a joint industry/Government team consisting of DOE, Glenn, and Lockheed Martin Astronautics. This team concluded that there are no technical reasons that would rule out using the Stirling converter for deep space missions. As a direct result of the successful testing at Glenn, the DOE/Stirling Technology Company 55-We Stirling converter has been baselined for the SRPS. Glenn is now continuing an in-house project to assist in developing the Stirling converter for readiness for space qualification and mission implementation. As part of this effort, the Stirling converter will be further characterized under launch environment random vibration testing, methods to reduce converter EMI will be developed, and an independent performance verification will be completed. Converter life assessment and permanent magnet aging characterization tasks are also underway. Substitute organic materials for the linear alternator and piston bearing coatings for use in a high-radiation environment have been identified and have now been incorporated in Stirling converters built by Stirling Technology Company for Glenn. Electromagnetic and thermal finite element analyses for the alternator are also being conducted.

Thieme, Lanny G.↗

Structural dynamic and aeroelastic considerations for hypersonic vehicles

Structural dynamic and aeroelastic considerations applicable to hypersonic vehicles are discussed. Emphasis is given to aerospace plane configurations. The definition of aerothermoelasticity and the operational flight environment are reviewed, and structural dynamic and aeroelastic areas of concern are individually discussed, including vibration, landing and taxiing, propellant dynamics, acoustics, lifting surface flutter, panel flutter, control surface buzz, buffeting, gust response, and static aeroelasticity. Recent research results from all-moveable delta-wing aerolastic studies, engine inlet lip aeroelastic analysis, and studies of thermal effects on vibration frequencies, aerodynamic heating effects on flutter, and active control of aeroelastic response are reviewed.

Cazier, F. W., Jr.↗

Measuring Segmented Primary Mirror WFE in the Presence of Vibration and Thermal Drift on the Light-Weighted JWST

The light-weighted design of the Optical Telescope Element (OTE) of the James Webb Telescope (JWST) leads to additional sensitivity to vibration from the ground - an important consideration to the measurement uncertainty of the wavefront error (WFE) in the primary mirror. Furthermore, segmentation of the primary mirror leads to rigid-body movements of segment areas in the WFE. The ground vibrations are minimized with modifications to the test facility, and by the architecture of the equipment supporting the load. Additional special test equipment (including strategically placed isolators, tunable mass dampers, and cryogenic magnetic dampers) mitigates the vibration and the response sensitivity before reaching the telescope. A multi-wavelength interferometer is designed and operated to accommodate the predicted residual vibration. Thermal drift also adds to the measurement variation. Test results of test equipment components, measurement theory, and finite element analysis combine to predict the test uncertainty in the future measurement of the primary mirror. The vibration input to the finite element model comes from accelerometer measurements of the facility with the environmental control pumps operating. One of the isolators have been built and tested to validate the dynamic performance. A preliminary model of the load support equipment and the OTE with the Integrated Science Instrument Module (ISIM) is complete. The performance of the add-on dampers have been established in previous applications. And operation of the multi-wavelength interferometer was demonstrated on a scaled hardware version of the JWST in an environment with vibration and thermal drift.

Whitman, Tony L.↗

CETA truck and EVA restraint system

The Crew Equipment Translation Aid (CETA) experiment is an extravehicular activity (EVA) Space Transportation System (STS) based flight experiment which will explore various modes of transporting astronauts and light equipment for Space Station Freedom (SSF). The basic elements of CETA are: (1) two 25 foot long sections of monorail, which will be EVA assembled in the STS cargo bay to become a single 50 ft. rail called the track; (2) a wheeled baseplate called the truck which rolls along the track and can accept three cart concepts; and (3) the three carts which are designated manual, electric, and mechanical. The three carts serve as the astronaut restraint and locomotive interfaces with the track. The manual cart is powered by the astronaut grasping the track's handrail and pulling himself along. The electric cart is operated by an astronaut turning a generator which powers the electric motor and drives the cart. The mechanical cart is driven by a Bendix type transmission and is similar in concept to a man-propelled railroad cart. During launch and landing, the truck is attached to the deployable track by means of EVA removable restraint bolts and held in position by a system of retractable shims. These shims are positioned on the exterior of the rail for launch and landing and rotate out of the way for the duration of the experiment. The shims are held in position by strips of Velcro nap, which rub against the sides of the shim and exert a tailored force. The amount of force required to rotate the shims was a major EVA concern, along with operational repeatability and extreme temperature effects. The restraint system was tested in a thermal-vac and vibration environment and was shown to meet all of the initial design requirements. Using design inputs from the astronauts who will perform the EVA, CETA evolved through an iterative design process and represented a cooperative effort.

Beals, David C.↗

In-service health monitoring of composite structures

The aerospace industry is witnessing a vast utilization of composites in critical structural applications and anticipates even more use of them in future aircraft. Therefore, a definite need exists for a composite health monitoring expert system to meet today's current needs and tomorrow's future demands. The primary goal for this conceptual health monitoring system is functional reliably for in-service operation in the environments of various composite structures. The underlying philosophy of this system is to utilize proven vibration techniques to assess the structural integrity of a fibrous composite. Statistical methods are used to determine if the variances in the measured data are acceptable for making a reliable decision on the health status of the composite. The flexible system allows for algorithms describing any composite fatigue or damage behavior characteristic to be provided as an input to the system. Alert thresholds and variances can also be provided as an input to this system and may be updated to allow for future changes/refinements in the composite's structural integrity behavior.

Pinto, Gino A.↗

Flow Energy Piezoelectric Bimorph Nozzle Harvester

There is a need for a long-life power generation scheme that could be used downhole in an oil well to produce 1 Watt average power. There are a variety of existing or proposed energy harvesting schemes that could be used in this environment but each of these has its own limitations. The vibrating piezoelectric structure is in principle capable of operating for very long lifetimes (decades) thereby possibly overcoming a principle limitation of existing technology based on rotating turbo-machinery. In order to determine the feasibility of using piezoelectrics to produce suitable flow energy harvesting, we surveyed experimentally a variety of nozzle configurations that could be used to excite a vibrating piezoelectric structure in such a way as to enable conversion of flow energy into useful amounts of electrical power. These included reed structures, spring mass-structures, drag and lift bluff bodies and a variety of nozzles with varying flow profiles. Although not an exhaustive survey we identified a spline nozzle/piezoelectric bimorph system that experimentally produced up to 3.4 mW per bimorph. This paper will discuss these results and present our initial analyses of the device using dimensional analysis and constitutive electromechanical modeling. The analysis suggests that an order-of-magnitude improvement in power generation from the current design is possible.

transducers↗

The Strata-l Experiment on Microgravity Regolith Segregation

The Strata-1 experiment studies the segregation of small-body regolith through long-duration exposure of simulant materials to the microgravity environment on the International Space Station (ISS). Many asteroids feature low bulk densities, which implies high values of porosity and a mechanical structure composed of loosely bound particles, (i.e. the "rubble pile" model), a prime example of a granular medium. Even the higher-density, mechanically coherent asteroids feature a significant surface layer of loose regolith. These bodies will evolve in response to very small perturbations such as micrometeoroid impacts, planetary flybys, and the YORP effect. A detailed understanding of asteroid mechanical evolution is needed in order to predict the surface characteristics of as-of-yet unvisited bodies, to understand the larger context of samples from sample return missions, and to mitigate risks for both manned and unmanned missions to asteroidal bodies. Due to observation of rocky regions on asteorids such as Eros and Itokawa, it has been hypothesized that grain size distribution with depth on an asteroid may be inhomogeneous: specifically, that large boulders have been mobilized to the surface. In terrestrial environments, this size-dependent sorting to the surface of the sample is called the Brazil Nut Effect. The microgravity and acceleration environment on the ISS is similar that of a small asteroid. Thus, Strata-1 investigates size segregation of regolith in an environment analogous to that of small bodies. Strata-1 consists of four regolith simulants in evacuated tubes, as shown in Figure 1 (Top and Middle). The simulants are (1) a crushed and sieved ordinary chondrite meteorite to simulate an asteroidal surface, (2) a carbonaceous chondrite simulant with a mixture of fine and course particles, and two simplified silicate glass simulants; (3) one with angular and (4) another with spherical particles. These materials were chosen to span a range of granular complexity. The materials were sorted into three size species pre-launch, and maintained during launch and return by a device called the Entrapulator. The hypothesis under test is that the particles that constitute a granular medium in a micro-gravity environment, subjected to a known vibration environemnt, will segregate in accordance to modeled predictions. Strata-1 is currently operating on ISS, with cameras capturing images of simulant motion throughout the one year mission. Vibration data is recorded and downlinked, and the simulants will be analyzed after return to Earth.

Fries, M.↗

Advanced Technology for Isolating Payloads in Microgravity

One presumption of scientific microgravity research is that while in space disturbances are minimized and experiments can be conducted in the absence of gravity. The problem with this assumption is that numerous disturbances actually occur in the space environment. Scientists must consider all disturbances when planning microgravity experiments. Although small disturbances, such as a human sneeze, do not cause most researchers on earth much concern, in space, these minuscule disturbances can be detrimental to the success or failure of an experiment. Therefore, a need exists to isolate experiments and provide a quiescent microgravity environment. The objective of microgravity isolation is to quantify all possible disturbances or vibrations and then attenuate the transmission of the disturbance to the experiment. Some well-defined vibration sources are: experiment operations, pumps, fans, antenna movements, ventilation systems and robotic manipulators. In some cases, it is possible to isolate the source using simple vibration dampers, shock absorbers and other isolation devices. The problem with simple isolation systems is that not all vibration frequencies are attenuated, especially frequencies less than 0.1 Hz. Therefore, some disturbances are actually emitted into the environment. Sometimes vibration sources are not well defined, or cannot be controlled. These include thermal "creak," random acoustic vibrations, aerodynamic drag, crew activities, and other similar disturbances. On some "microgravity missions," such as the United States Microgravity Laboratory (USML) and the International Microgravity Laboratory (IML) missions, the goal was to create extended quiescent times and limit crew activity during these times. This might be possible for short periods, but for extended durations it is impossible due to the nature of the space environment. On the International Space Station (ISS), vehicle attitude readjustments are required to keep the vehicle in a minimum torque orientation and other experimental activities will occur continually, both inside and outside the station. Since all vibration sources cannot be controlled, the task of attenuating the disturbances is the only realistic alternative. Several groups have independently developed technology to isolate payloads from the space environment. Since 1970, Honeywell's Satellite Systems Division has designed several payload isolation systems and vibration attenuators. From 1987 to 1992, NASA's Lewis Research Center (LeRC) performed research on isolation technology and developed a 6 degree-of-freedom (DOF) isolator and tested the system during 70 low gravity aircraft flight trajectories. Beginning in early 1995, NASA's Marshall Space Flight Center (MSFC) and McDonnell Douglas Aerospace (MDA) jointly developed the STABLE (Suppression of Transient Accelerations By Levitation Evaluation) isolation system. This 5 month accelerated effort produced the first flight of an active microgravity vibration isolation system on STS-73/USML-02 in late October 1995. The Canadian Space Agency developed the Microgravity Vibration Isolation Mount (MIM) for isolating microgravity payloads and this system began operating on the Russian Mir Space Station in May 1996. The Boeing Defense & Space Group, Missiles & Space Division developed the Active Rack Isolation System (ARIS) for isolating payloads in a standard payload rack. ARIS was tested in September 1996 during the STS-79 mission to Mir. Although these isolation systems differ in their technological approach, the objective is to isolate payloads from disturbances. The following sections describe the technologies behind these systems and the different types of hardware used to perform isolation. The purpose of these descriptions is not to detail the inner workings of the hardware but to give the reader an idea of the technology and uses of the hardware components. Also included in the component descriptions is a paragraph detailing some of the advances in isolation technology for that particular component. The final section presents some concluding thoughts and a summary of anticipated advances in research and development for isolating microgravity experiments.

Alhorn, Dean C.↗

Utilizing Advanced Vibration Isolation Technology to Enable Microgravity Science Operations

Microgravity scientific research is performed in space to determine the effects of gravity upon experiments. Until recently, experiments had to accept the environment aboard various carriers: reduced-gravity aircraft, sub-orbital payloads, Space Shuttle, and Mir. If the environment is unacceptable, then most scientists would rather not expend the resources without the assurance of true microgravity conditions. This is currently the case on the International Space Station, because the ambient acceleration environment will exceed desirable levels. For this reason, the g-LIMIT (Glovebox Integrated Microgravity Isolation Technology) system is currently being developed to provide a quiescent acceleration environment for scientific operations. This sub-rack isolation system will provide a generic interface for a variety of experiments for the Microgravity Science Glovebox. This paper describes the motivation for developing of the g-LIMIT system, presents the design concept and details some of the advanced technologies utilized in the g-LIMIT flight design.

Alhorn, Dean Carl↗

Dynamic Loads Generation for Multi-Point Vibration Excitation Problems

A random-force method has been developed to predict dynamic loads produced by rocket-engine random vibrations for new rocket-engine designs. The method develops random forces at multiple excitation points based on random vibration environments scaled from accelerometer data obtained during hot-fire tests of existing rocket engines. This random-force method applies random forces to the model and creates expected dynamic response in a manner that simulates the way the operating engine applies self-generated random vibration forces (random pressure acting on an area) with the resulting responses that we measure with accelerometers. This innovation includes the methodology (implementation sequence), the computer code, two methods to generate the random-force vibration spectra, and two methods to reduce some of the inherent conservatism in the dynamic loads. This methodology would be implemented to generate the random-force spectra at excitation nodes without requiring the use of artificial boundary conditions in a finite element model. More accurate random dynamic loads than those predicted by current industry methods can then be generated using the random force spectra. The scaling method used to develop the initial power spectral density (PSD) environments for deriving the random forces for the rocket engine case is based on the Barrett Criteria developed at Marshall Space Flight Center in 1963. This invention approach can be applied in the aerospace, automotive, and other industries to obtain reliable dynamic loads and responses from a finite element model for any structure subject to multipoint random vibration excitations.

Shen, Lawrence↗