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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Forward rotor vortex effects on counter rotating propeller noise

Three configurations of a model counter rotating propeller manipulate the blade tip flow by: placing the CRP at angle of attack, installing shrouds, and turning the upstream blades to provide forward sweep. Flow visualization and flow measurements with thermal anemometry show no evidence of a tip vortex; however, a leading edge vortex was detected on aft swept blades. The modifications served to alter the strength and/or path of the leading edge vortex. The vortical flow is eliminated by forward sweep on the upstream propeller blades. Far field acoustic data from each test indicate only small influences on the level and directivity of the BPFs. The interaction tone at the sum of the two BPF's was significantly altered in a consistent manner. As the vortex system varied, the interaction tone was affected: far field noise levels in the forward quandrant increased and the characteristic noise minimum near the plane of rotation became less pronounced and in some cases were eliminated. If the forward propeller leading edge vortex system does not impact the rear propeller in the standard manner, a net increase in the primary interaction tone occurs for the model tested. If the leading edge vortex is removed, the interaction tone increases.

Laur, Michele↗
NASA NTRS1994

A hydrodynamic approach to cosmology: The mixed dark matter cosmological scenario

We compute the evolution of spatially flat, mixed cold and hot dark matter models containing both baryonic matter and two kinds of dark matter. Hydrodynamics is treated with a highly developed Eulerian hydrodynamic code (see Cen 1992). A standard particle-mesh (PM) code is also used in parallel to calculate the motion of the dark matter components. We adopt the following parameters: h equivalent to (sub 0)/100 km/s Mpc(exp -1) = 0.5, OMEGA(sub C) = 0.3, and OMEGA(sub B) = 0.06, with amplitude of the perturbation spectrum fixed by the Cosmic Background Explorer Satellite (COBE) Dark Matter Radiation (DMR) measurements (Smoot et al. 1992) being sigma (sub 8) = 0.67. Four different boxes are simulated with box sizes of L = (64, 16, 4, 1) h(exp -1) Mpc, respectively, the two small boxes providing good resolution but little valid information due to absence of large-scale power. We use 128(exp 3) approximate 10(exp 6.3) baryonic cells, 128(exp .3) cold dark matter particles, and 2 x 128(exp 3) hot dark matter particles. In addition to the dark matter we follow separately six baryonic species (H, H(+), He, He(+), He(++), e(-)) with allowance for both (nonequilibrium) collisional and radiative ionization in every cell. The background radiation field is also followed in detail with allowance made for both continuum and line processes, to allow nonequilibrium heating and cooling processes to be followed in detail. The mean final Zeldovich-Sunyaev y parameter is estimated to be y Bar = (5.4 + or - 2.7) x 10(exp -7) below currently attainable observations, with a rms fluctuation of approximately delta bar y = (0.6 + or - 3.0) x 10(exp -7) on arcminute scales. The rate of galaxy formation peaks at an even later epoch (z approximate 0.3) than in the standard (OMEGA = 1, sigma sub 8 = 0.67) cold dark matter (CDM) model (z approximate 0.5) and, at a redshift of z = 4, is nearly a factor of 100 lower than for the CDM model with the same value of sigma sub 8. With regard to mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum has a broad peak in the vicinity of M(sub B) = 10(exp 9.5) solar mass with a reasonable fit to the Schechter luminosity function if the ratio of baryon mass to blue light is approximately 4. In addition, one very large PM simulation was made in a box with size (320 h(exp - 1) Mpc) containing 3 x 200(exp 3) = 10(exp 7.4) particles. Utilizing this simulation we find that the model yields a cluster mass function which is about a factor of 4 higher than observed, but a cluster-cluster correlation length marginally lower than observed, but that both are closer to observations than in the (COBE) normalized CDM model. The one-dimensional pairwise velocity dispersion is 605 + or - 8 km/s at 1/h separation, lower than that of the DCM model normalized to COBE, but still significant higher than observations (Davis & Peebles 1983). A plausible velocity bias b(sub v) = 0.8 + or - 0.1 on this scale will reduce but not remove the discrepancy. The velocity auto-correlat ion function has a coherence length of 40/h Mpc, which is somewhat lower than the observed counterpart. In all these respects the model would be improved by decreasing the cold fraction of the dark OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDB). But formation of galaxies and clusters of galaxies is much later in this model than in COBE-normalized CDM, perhaps too late. To improve on these constraints a larger ratio of OMEGA(sub CDM)/ (OMEGA(sub CDM) + OMEGA(sub HDM)) is required than the value of 0.67 adopted here. It does not seem possible to find a value for this ratio which would satisfy all tests. Overall, the model is similar both on large and intermediate scales to the standard CDM model normalized to the same value of sigma(sub B), but the problem with regard to late formation of galaxies is more severe in this model than in that CDM model. Adding hot dark matter, significantly improves the ability of the COBE-normalized CDM scenario to fit existing observations, but the model is in fact not as good as the CDM model with the same sigma(sub 8) and is still probably unsatisfactory with regard to several critical tests.

Cen, Renyue↗
NASA NTRS2012

Evaluation of Advanced Stirling Convertor Net Heat Input Correlation Methods Using a Thermal Standard

The U.S. Department of Energy (DOE) and Lockheed Martin Space Systems Company (LMSSC) have been developing the Advanced Stirling Radioisotope Generator (ASRG) for use as a power system for space science missions. This generator would use two high-efficiency Advanced Stirling Convertors (ASCs), developed by Sunpower Inc. and NASA Glenn Research Center (GRC). The ASCs convert thermal energy from a radioisotope heat source into electricity. As part of ground testing of these ASCs, different operating conditions are used to simulate expected mission conditions. These conditions require achieving a particular operating frequency, hot end and cold end temperatures, and specified electrical power output for a given net heat input. In an effort to improve net heat input predictions, numerous tasks have been performed which provided a more accurate value for net heat input into the ASCs, including testing validation hardware, known as the Thermal Standard, to provide a direct comparison to numerical and empirical models used to predict convertor net heat input. This validation hardware provided a comparison for scrutinizing and improving empirical correlations and numerical models of ASC-E2 net heat input. This hardware simulated the characteristics of an ASC-E2 convertor in both an operating and non-operating mode. This paper describes the Thermal Standard testing and the conclusions of the validation effort applied to the empirical correlation methods used by the Radioisotope Power System (RPS) team at NASA Glenn.

Briggs, Maxwell H.↗
NASA NTRS2009

Investigation of Seal-to-Floor Effects on Semi-Span Transonic Models

In an effort to achieve the maximum possible Reynolds number (Re) when conducting production testing for flight loads aerodynamic databases, it has been the preferred practice of The Boeing Company / Commercial Airplanes (BCA) -- Loads and Dynamics Group since the early 1990's to test large scale semi-span models in the 11- By 11-Foot Transonic Wind Tunnel (TWT) leg of the Unitary Plan Wind Tunnel (UPWT) at the NASA Ames Research Center (ARC). There are many problems related to testing large scale semi-span models of high aspect ratio flexible transport wings, such as; floor boundary layer effects, wing spanwise wall effects, solid blockage buoyancy effects, floor mechanical interference effects, airflow under the model effects, or tunnel flow gradient effects. For most of these issues, BCA has developed and implemented either standard testing methods or numerical correction schemes and these will not be discussed in this document. Other researchers have reported on semi-span transonic testing correction issues, however most of the reported research has been for low Mach testing. Some of the reports for low Mach testing address the difficult problem of preventing undesirable airflow under a semi-span model while ensuring unrestricted main balance functionality, however, for transonic models this issue has gone unresolved. BCA has been cognizant for sometime that there are marked differences in wing pressure distributions from semi-span transonic model testing than from full model or flight testing. It has been suspected that these differences are at least in part due to airflow under the model. Previous efforts by BCA to address this issue have proven to be ineffective or inconclusive and in one situation resulted in broken hardware. This paper reports on a Boeing-NASA collaborative investigation based on a series of small tests conducted between June 2006 and November 2007 in the 11 by 11 foot Transonic Wind Tunnel at NASA Ames on three large commercial jet transport configurations to assess the effects of sealing a semi-span model to the floor and to investigate efficient sealing and testing techniques. This document will show how sealing the model to the floor has a small but remarkably far reaching spanwise effect on wing pressures, wing local section forces and wing force summations.

Sleppy, Mark A.↗
NASA NTRS2011

NASA Occupant Protection Standards Development

Current National Aeronautics and Space Administration (NASA) occupant protection standards and requirements are based on extrapolations of biodynamic models, which were based on human tests performed under pre-Space Shuttle human flight programs where the occupants were in different suit and seat configurations than is expected for the Multi Purpose Crew Vehicle (MPCV) and Commercial Crew programs. As a result, there is limited statistical validity to the occupant protection standards. Furthermore, the current standards and requirements have not been validated in relevant spaceflight suit, seat configurations or loading conditions. The objectives of this study were to develop new standards and requirements for occupant protection and rigorously validate these new standards with sub-injurious human testing. To accomplish these objectives we began by determining which critical injuries NASA would like to protect for. We then defined the anthropomorphic test device (ATD) and the associated injury metrics of interest. Finally, we conducted a literature review of available data for the Test Device for Human Occupant Restraint New Technology (THOR-NT) ATD to determine injury assessment reference values (IARV) to serve as a baseline for further development. To better understand NASA s environment, we propose conducting sub-injurious human testing in spaceflight seat and suit configurations with spaceflight dynamic loads, with a sufficiently high number of subjects to validate no injury during nominal landing loads. In addition to validate nominal loads, the THOR-NT ATD will be tested in the same conditions as the human volunteers, allowing correlation between human and ATD responses covering the Orion nominal landing environment and commercial vehicle expected nominal environments. All testing will be conducted without the suit and with the suit to ascertain the contribution of the suit to human and ATD responses. In addition to the testing campaign proposed, additional data analysis is proposed to mine existing human injury and response data from other sources, including military volunteer testing, automotive Crash Injury Research Engineering Network (CIREN), and IndyCar impact and injury data. These data sources can allow a better extrapolation of the ATD responses to off-nominal conditions above the nominal range that can safely be tested. These elements will be used to develop injury risk functions for each of the injury metrics measured from the ATD. These risk functions would serve as the basis for the NASA standards. Finally, we propose defining standard test methodology for evaluating future spacecraft designs against the IARVs, including developing a star-rating system to allow crew safety comparisons between vehicles.

Somers, Jeffrey T.↗
NASA NTRS1988

Evapotranspiration from nonuniform surfaces - A first approach for short-term numerical weather prediction

Observations of surface heterogeneity of soil moisture from scales of meters to hundreds of kilometers are discussed, and a relationship between grid element size and soil moisture variability is presented. An evapotranspiration model is presented which accounts for the variability of soil moisture, standing surface water, and vegetation internal and stomatal resistance to moisture flow from the soil. The mean values and standard deviations of these parameters are required as input to the model. Tests of this model against field observations are reported, and extensive sensitivity tests are presented which explore the importance of including subgrid-scale variability in an evapotranspiration model.

Wetzel, Peter J.↗
NASA NTRS1988

Modelling the performance of the tapered artery heat pipe design for use in the radiator of the solar dynamic power system of the NASA Space Station

The paper presents a computer program developed to model the steady-state performance of the tapered artery heat pipe for use in the radiator of the solar dynamic power system of the NASA Space Station. The program solves six governing equations to ascertain which one is limiting the maximum heat transfer rate of the heat pipe. The present model appeared to be slightly better than the LTV model in matching the 1-g data for the standard 15-ft test heat pipe.

Evans, Austin Lewis↗
NASA NTRS1990

Modal analysis of UH-60A instrumented rotor blades

The dynamic characteristics of instrumented and production UH-60A Black Hawk main rotor blades were measured, and the results were validated with NASTRAN finite element models. The blades tested included pressure and strain-gage instrumented blades, which are part of the NASA Airloads Flight Research Phase of the Modern Technology Rotor Program. The dynamic similarity of the blades was required for accurate data collection in this program. Therefore, a nonrotating blade modal analysis was performed on the first 10 free-free modes to measure blade similarities. The results showed small differences between the modal frequencies of instrumented and production blades and a close correlation with the NASTRAN models. This type of modal testing and analysis is recommended as a standard procedure for future instrumented blade flight testing.

Hamade, Karen S.↗
NASA NTRS1990

Modal analysis of UH 60A instrumented rotor blades

The dynamic characteristics of instrumented and production UH-60A Black Hawk main rotor blades were measured, and the results were validated with NASTRAN finite element models. The blades tested included pressure and strain-gage instrumented blades which are part of NASA's Airloads Flight Research Phase of the Modern Technology Rotor Program. The dynamic similarity of the blades was required for accurate data collection in this program. Therefore, a nonrotating blade modal analysis was performed on the first 10 free-free modes to measure blade similarities. The results showed small differences between the modal frequencies of instrumented and production blades and a close correlation with the NASTRAN models. This type of modal testing and analysis is recommended as a standard procedure for future instrumented blade flight testing.

Hamade, Karen S.↗
NASA NTRS1995

A fully associative, nonisothermal, nonlinear kinematic, unified viscoplastic model for titanium alloys

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential base multiaxial, nonisothermal unified viscoplastic model is obtained. This model possesses one tensorial internal state variable (that is, associated with dislocation substructure) and an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of nonlinear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This nonlinear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated), greatly influences the multiaxial response under non-proportional loading paths, and in the case of nonisothermal histories, introduces an instantaneous thermal softening mechanism proportional to the rate of change in temperature. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. The specific model proposed is characterized for a representative titanium alloy commonly used as the matrix material in SiC fiber reinforced composites, i.e., TIMETAL 21S. Verification of the proposed model is shown using 'specialized' non-standard isothermal and thermomechanical deformation tests.

Arnold, S. M.↗
NASA NTRS2002

A Rewriting-Based Approach to Trace Analysis

We present a rewriting-based algorithm for efficiently evaluating future time Linear Temporal Logic (LTL) formulae on finite execution traces online. While the standard models of LTL are infinite traces, finite traces appear naturally when testing and/or monitoring red applications that only run for limited time periods. The presented algorithm is implemented in the Maude executable specification language and essentially consists of a set of equations establishing an executable semantics of LTL using a simple formula transforming approach. The algorithm is further improved to build automata on-the-fly from formulae, using memoization. The result is a very efficient and small Maude program that can be used to monitor program executions. We furthermore present an alternative algorithm for synthesizing probably minimal observer finite state machines (or automata) from LTL formulae, which can be used to analyze execution traces without the need for a rewriting system, and can hence be used by observers written in conventional programming languages. The presented work is part of an ambitious runtime verification and monitoring project at NASA Ames, called PATHEXPLORER, and demonstrates that rewriting can be a tractable and attractive means for experimenting and implementing program monitoring logics.

Havelund, Klaus↗
NASA NTRS2014

The Atacama Cosmology Telescope: Temperature and Gravitational Lensing Power Spectrum Measurements from Three Seasons of Data

We present the temperature power spectra of the cosmic microwave background (CMB) derived from the three seasons of data from the Atacama Cosmology Telescope (ACT) at 148 GHz and 218 GHz, as well as the cross-frequency spectrum between the two channels. We detect and correct for contamination due to the Galactic cirrus in our equatorial maps. We present the results of a number of tests for possible systematic error and conclude that any effects are not significant compared to the statistical errors we quote. Where they overlap, we cross-correlate the ACT and the South Pole Telescope (SPT) maps and show they are consistent. The measurements of higher-order peaks in the CMB power spectrum provide an additional test of the ΛCDM cosmological model, and help constrain extensions beyond the standard model. The small angular scale power spectrum also provides constraining power on the Sunyaev-Zel'dovich effects and extragalactic foregrounds. We also present a measurement of the CMB gravitational lensing convergence power spectrum at 4.6σ detection significance.

Atacama Cosmology Telescope (ACT)↗
NASA NTRS2021

High Angular Resolution Gravitational Wave Astronomy

Since the very beginning of astronomy the location of objects on the sky has been a fundamental observational quantity that has been taken for granted. While precise two dimensional positional information is easy to obtain for observations in the electromagnetic spectrum, the positional accuracy of current and near future gravitational wave detectors is limited to between tens and hundreds of square degrees, which makes it extremely challenging to identify the host galaxies of gravitational wave events or to detect any electromagnetic counterparts. Gravitational wave observations provide information on source properties that is complementary to the information in any associated electromagnetic emission. Observing systems with multiple messengers thus has scientific potential much greater than the sum of its parts. A gravitational wave detector with higher angular resolution would significantly increase the prospects for finding the hosts of gravitational wave sources and triggering a multi-messenger follow-up campaign. An observatory with arcminute precision or better could be realised within the Voyage 2050 programme by creating a large baseline interferometer array in space and would have transformative scientific potential. Precise positional information of standard sirens would enable precision measurements of cosmological parameters and offer new insights on structure formation; a high angular resolution gravitational wave observatory would allow the detection of a stochastic background and resolution of the anisotropies within it; it would also allow the study of accretion processes around black holes; and it would have tremendous potential for tests of modified gravity and the discovery of physics beyond the Standard Model.

Gravitational waves↗
NASA NTRS2013

Pressure-Sensitive Paints Advance Rotorcraft Design Testing

The rotors of certain helicopters can spin at speeds as high as 500 revolutions per minute. As the blades slice through the air, they flex, moving into the wind and back out, experiencing pressure changes on the order of thousands of times a second and even higher. All of this makes acquiring a true understanding of rotorcraft aerodynamics a difficult task. A traditional means of acquiring aerodynamic data is to conduct wind tunnel tests using a vehicle model outfitted with pressure taps and other sensors. These sensors add significant costs to wind tunnel testing while only providing measurements at discrete locations on the model's surface. In addition, standard sensor solutions do not work for pulling data from a rotor in motion. "Typical static pressure instrumentation can't handle that," explains Neal Watkins, electronics engineer in Langley Research Center s Advanced Sensing and Optical Measurement Branch. "There are dynamic pressure taps, but your costs go up by a factor of five to ten if you use those. In addition, recovery of the pressure tap readings is accomplished through slip rings, which allow only a limited amount of sensors and can require significant maintenance throughout a typical rotor test." One alternative to sensor-based wind tunnel testing is pressure sensitive paint (PSP). A coating of a specialized paint containing luminescent material is applied to the model. When exposed to an LED or laser light source, the material glows. The glowing material tends to be reactive to oxygen, explains Watkins, which causes the glow to diminish. The more oxygen that is present (or the more air present, since oxygen exists in a fixed proportion in air), the less the painted surface glows. Imaged with a camera, the areas experiencing greater air pressure show up darker than areas of less pressure. "The paint allows for a global pressure map as opposed to specific points," says Watkins. With PSP, each pixel recorded by the camera becomes an optical pressure tap. "Instead of having 100 or 200 pressure taps, you can have in theory several million, up to whatever the resolution of your camera is." Watkins explains that typical wind tunnel testing requires two models: one with very little instrumentation, and a pressure model with a significant amount of sensors applied. "If you can make all of your measurements on one model with PSP, you've decreased your model costs by at least a factor of two and preferably your testing costs by about that much," he says. PSP technology has been around for almost 20 years, but a PSP solution for gathering instantaneous dynamic pressure data from surfaces moving at high speeds, such as rotor blades, was not available until a NASA partnership led to a game-changing innovation.

Source record↗
NASA NTRS2016

UAS Integration in the NAS Project: Flight Test 3 Data Analysis of JADEM-Autoresolver Detect and Avoid System

The Unmanned Aircraft Systems Integration in the National Airspace System project, or UAS Integration in the NAS, aims to reduce technical barriers related to safety and operational challenges associated with enabling routine UAS access to the NAS. The UAS Integration in the NAS Project conducted a flight test activity, referred to as Flight Test 3 (FT3), involving several Detect-and-Avoid (DAA) research prototype systems between June 15, 2015 and August 12, 2015 at the Armstrong Flight Research Center (AFRC). This report documents the flight testing and analysis results for the NASA Ames-developed JADEM-Autoresolver DAA system, referred to as 'Autoresolver' herein. Four flight test days (June 17, 18, 22, and July 22) were dedicated to Autoresolver testing. The objectives of this test were as follows: 1. Validate CPA prediction accuracy and detect-and-avoid (DAA, formerly known as self-separation) alerting logic in realistic flight conditions. 2. Validate DAA trajectory model including maneuvers. 3. Evaluate TCAS/DAA interoperability. 4. Inform final Minimum Operating Performance Standards (MOPS). Flight test scenarios were designed to collect data to directly address the objectives 1-3. Objective 4, inform final MOPS, was a general objective applicable to the UAS in the NAS project as a whole, of which flight test is a subset. This report presents analysis results completed in support of the UAS in the NAS project FT3 data review conducted on October 20, 2015. Due to time constraints and, to a lesser extent, TCAS data collection issues, objective 3 was not evaluated in this analysis.

flight test↗
NASA NTRS2005

Assessment of Technologies for the Space Shuttle External Tank Thermal Protection System and Recommendations for Technology Improvement - Part III: Material Property Characterization, Analysis, and Test Methods

The objective of this report is to contribute to the independent assessment of the Space Shuttle External Tank Foam Material. This report specifically addresses material modeling, characterization testing, data reduction methods, and data pedigree. A brief description of the External Tank foam materials, locations, and standard failure modes is provided to develop suitable background information. A review of mechanics based analysis methods from the open literature is used to provide an assessment of the state-of-the-art in material modeling of closed cell foams. Further, this report assesses the existing material property database and investigates sources of material property variability. The report presents identified deficiencies in testing methods and procedures, recommendations for additional testing as required, identification of near-term improvements that should be pursued, and long-term capabilities or enhancements that should be developed.

Gates, Thomas S.↗
NASA NTRS1973

Atmospheric model for correction of spacecraft data.

Description of a radiative transfer model which has been used to correct Apollo photographic imagery for degradation arising from atmospheric scattering. The model was tested using aircraft scanner data, and an extrapolation was then made to spacecraft altitudes. Using standard meteorological data for the region of interest, it is possible to determine transmittance, path radiance, and total radiance from calculations made with the multiple scattering atmospheric model. Simple algorithms are presented which allow potential users of spacecraft sensor data to correct imagery for the deleterious effects due to the scattering of radiation under clear or hazy atmospheric conditions.

Turner, R. E.↗
NASA NTRS2018

Comparing Free-Free and Shaker Table Model Correlation Methods Using Jim Beam

Finite element model correlation as part of a spacecraft program has always been a challenge. For any NASA mission, the coupled system response of the spacecraft and launch vehicle can be determined analytically through a Coupled Loads Analysis (CLA), as it is not possible to test the spacecraft and launch vehicle coupled system before launch. The value of the CLA is highly dependent on the accuracy of the frequencies and mode shapes extracted from the spacecraft model. NASA standards require the spacecraft model used in the final Verification Loads Cycle to be correlated by either a modal test or by comparison of the model with Frequency Response Functions (FRFs) obtained during the environmental qualification test. Due to budgetary and time constraints, most programs opt to correlate the spacecraft dynamic model during the environmental qualification test, conducted on a large shaker table. For any model correlation effort, the key has always been finding a proper definition of the boundary conditions. This paper is a correlation case study to investigate the difference in responses of a simple structure using a free-free boundary, a fixed boundary on the shaker table, and a base-drive vibration test, all using identical instrumentation. The NAVCON Jim Beam test structure, featured in the IMAC round robin modal test of 2009, was selected as a simple, well recognized and well characterized structure to conduct this investigation. First, a free-free impact modal test of the Jim Beam was done as an experimental control. Second, the Jim Beam was mounted to a large 20,000 lbf shaker, and an impact modal test in this fixed configuration was conducted. Lastly, a vibration test of the Jim Beam was conducted on the shaker table. The free-free impact test, the fixed impact test, and the base-drive test were used to assess the effect of the shaker modes, evaluate the validity of fixed-base modeling assumptions, and compare final model correlation results between these boundary conditions.

Modal Test↗