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NASA NTRS1993

Structural similitude and design of scaled down laminated models

The excellent mechanical properties of laminated composite structures make them prime candidates for wide variety of applications in aerospace, mechanical and other branches of engineering. The enormous design flexibility of advanced composites is obtained at the cost of large number of design parameters. Due to complexity of the systems and lack of complete design based informations, designers tend to be conservative in their design. Furthermore, any new design is extensively evaluated experimentally until it achieves the necessary reliability, performance and safety. However, the experimental evaluation of composite structures are costly and time consuming. Consequently, it is extremely useful if a full-scale structure can be replaced by a similar scaled-down model which is much easier to work with. Furthermore, a dramatic reduction in cost and time can be achieved, if available experimental data of a specific structure can be used to predict the behavior of a group of similar systems. This study investigates problems associated with the design of scaled models. Such study is important since it provides the necessary scaling laws, and the factors which affect the accuracy of the scale models. Similitude theory is employed to develop the necessary similarity conditions (scaling laws). Scaling laws provide relationship between a full-scale structure and its scale model, and can be used to extrapolate the experimental data of a small, inexpensive, and testable model into design information for a large prototype. Due to large number of design parameters, the identification of the principal scaling laws by conventional method (dimensional analysis) is tedious. Similitude theory based on governing equations of the structural system is more direct and simpler in execution. The difficulty of making completely similar scale models often leads to accept certain type of distortion from exact duplication of the prototype (partial similarity). Both complete and partial similarity are discussed. The procedure consists of systematically observing the effect of each parameter and corresponding scaling laws. Then acceptable intervals and limitations for these parameters and scaling laws are discussed. In each case, a set of valid scaling factors and corresponding response scaling laws that accurately predict the response of prototypes from experimental models is introduced. The examples used include rectangular laminated plates under destabilizing loads, applied individually, vibrational characteristics of same plates, as well as cylindrical bending of beam-plates.

Simitses, G. J.↗

NASA NTRS1979

Gyrodampers for large space structures

The problem of controlling the vibrations of a large space structures by the use of actively augmented damping devices distributed throughout the structure is addressed. The gyrodamper which consists of a set of single gimbal control moment gyros which are actively controlled to extract the structural vibratory energy through the local rotational deformations of the structure, is described and analyzed. Various linear and nonlinear dynamic simulations of gyrodamped beams are shown, including results on self-induced vibrations due to sensor noise and rotor imbalance. The complete nonlinear dynamic equations are included. The problem of designing and sizing a system of gyrodampers for a given structure, or extrapolating results for one gyrodamped structure to another is solved in terms of scaling laws. Novel scaling laws for gyro systems are derived, based upon fundamental physical principles, and various examples are given.

Aubrun, J. N.↗

NASA NTRS1982

Estimates of crater size for large-body impact Gravity-scaling results

A scaling analysis based upon dimensional invariance is used in conjunction with centrifuge experiments to estimate cratering efficiency as a function of impact velocity for kilometer-sized impactors. Complementing earlier, conventional small-scale impact experiments, centrifuge experiments were performed to substantiate these scaling laws in a scaled-size regime of interest. This technique provided empirical scaling laws used to estimate crater size for large bodies impacting the earth. From these scaling laws a 10-km-diameter body impacting at 25 km/s would be expected to produce a 66-km-diameter crater and to inject approximately 12 times its mass into the atmosphere.

Schmidt, R. M.↗

NASA NTRS1988

Crater size estimates for large-body terrestrial impact

Calculating the effects of impacts leading to global catastrophes requires knowledge of the impact process at very large size scales. This information cannot be obtained directly but must be inferred from subscale physical simulations, numerical simulations, and scaling laws. Schmidt and Holsapple presented scaling laws based upon laboratory-scale impact experiments performed on a centrifuge (Schmidt, 1980 and Schmidt and Holsapple, 1980). These experiments were used to develop scaling laws which were among the first to include gravity dependence associated with increasing event size. At that time using the results of experiments in dry sand and in water to provide bounds on crater size, they recognized that more precise bounds on large-body impact crater formation could be obtained with additional centrifuge experiments conducted in other geological media. In that previous work, simple power-law formulae were developed to relate final crater diameter to impactor size and velocity. In addition, Schmidt (1980) and Holsapple and Schmidt (1982) recognized that the energy scaling exponent is not a universal constant but depends upon the target media. Recently, Holsapple and Schmidt (1987) includes results for non-porous materials and provides a basis for estimating crater formation kinematics and final crater size. A revised set of scaling relationships for all crater parameters of interest are presented. These include results for various target media and include the kinematics of formation. Particular attention is given to possible limits brought about by very large impactors.

Schmidt, Robert M.↗

NASA NTRS1996

Inertial Range Dynamics in Boussinesq Turbulence

L'vov and Falkovich have shown that the dimensionally possible inertial range scaling laws for Boussinesq turbulence, Kolmogorov and Bolgiano scaling, describe steady states with constant flux of kinetic energy and of entropy respectively. These scaling laws are treated as similarity solutions of the direct interaction approximation for Boussinesq turbulence. The Kolmogorov scaling solution corresponds to a weak perturbation by gravity of a state in which the temperature is a passive scalar but in which a source of temperature fluctuations exists. Using standard inertial range balances, the renormalized viscosity and conductivity, turbulent Prandtl number, and spectral scaling law constants are computed for Bolgiano scaling.

Rubinstein, Robert↗

NASA NTRS2001

Transverse Tension Fatigue Life Characterization Through Flexure Testing of Composite Materials

The transverse tension fatigue life of S2/8552 glass-epoxy and IM7/8552 carbon-epoxy was characterized using flexure tests of 90-degree laminates loaded in 3-point and 4-point bending. The influence of specimen polishing and specimen configuration on transverse tension fatigue life was examined using the glass-epoxy laminates. Results showed that 90-degree bend specimens with polished machined edges and polished tension-side surfaces, where bending failures where observed, had lower fatigue lives than unpolished specimens when cyclically loaded at equal stress levels. The influence of specimen thickness and the utility of a Weibull scaling law was examined using the carbon-epoxy laminates. The influence of test frequency on fatigue results was also documented for the 4-point bending configuration. A Weibull scaling law was used to predict the 4-point bending fatigue lives from the 3-point bending curve fit and vice-versa. Scaling was performed based on maximum cyclic stress level as well as fatigue life. The scaling laws based on stress level shifted the curve fit S-N characterizations in the desired direction, however, the magnitude of the shift was not adequate to accurately predict the fatigue lives. Furthermore, the scaling law based on fatigue life shifted the curve fit S-N characterizations in the opposite direction from measured values. Therefore, these scaling laws were not adequate for obtaining accurate predictions of the transverse tension fatigue lives.

OBrien, T. Kevin↗

NASA NTRS1977

Concepts and methods for describing critical phenomena in fluids

The predictions of theoretical models for a critical-point phase transistion in fluids, namely the classical equation with third-degree critical isotherm, that with fifth-degree critical isotherm, and the lattice gas, are reviewed. The renormalization group theory of critical phenomena and the hypothesis of universality of critical behavior supported by this theory are discussed as well as the nature of gravity effects and how they affect cricital-region experimentation in fluids. The behavior of the thermodynamic properties and the correlation function is formulated in terms of scaling laws. The predictions of these scaling laws and of the hypothesis of universality of critical behavior are compared with experimental data for one-component fluids and it is indicated how the methods can be extended to describe critical phenomena in fluid mixtures.

Sengers, J. V.↗

NASA NTRS2010

Similarity Rules for Scaling Solar Sail Systems

Future science missions will require solar sails on the order of 200 square meters (or larger). However, ground demonstrations and flight demonstrations must be conducted at significantly smaller sizes, due to limitations of ground-based facilities and cost and availability of flight opportunities. For this reason, the ability to understand the process of scalability, as it applies to solar sail system models and test data, is crucial to the advancement of this technology. This paper will approach the problem of scaling in solar sail models by developing a set of scaling laws or similarity criteria that will provide constraints in the sail design process. These scaling laws establish functional relationships between design parameters of a prototype and model sail that are created at different geometric sizes. This work is applied to a specific solar sail configuration and results in three (four) similarity criteria for static (dynamic) sail models. Further, it is demonstrated that even in the context of unique sail material requirements and gravitational load of earth-bound experiments, it is possible to develop appropriate scaled sail experiments. In the longer term, these scaling laws can be used in the design of scaled experimental tests for solar sails and in analyzing the results from such tests.

Canfield, Stephen L.↗

NASA NTRS2023

Revisiting Empirical Solar Energetic Particle Scaling Relations. I. Solar Flares

Aims. The possible influence of solar superflares on the near-Earth space radiation environment are assessed through the investigation of scaling laws between the peak proton flux and fluence of solar energetic particle (SEP) events with the solar flare soft X-ray peak photon flux. Methods. We compiled a catalog of 65 well-connected (W20-90) SEP events during the last three solar cycles covering a period of ∼34 yr (1984–2020) that were associated with flares of class ≥C6.0, and investigated the statistical relations between the recorded peak proton fluxes (I p ) and the fluences (F p ) at a set of integral energies from E > 10, > 30, and > 60 to > 100 MeV versus the associated solar flare peak soft X-ray flux in the 1–8 Å band (F SXR ). Based on the inferred relations, we calculated the integrated energy dependence of the peak proton flux (I p ) and fluence (F p ) of the SEP events, assuming that they follow an inverse power law with respect to energy. Finally, we made use of simple physical assumptions, combining our derived scaling laws, and estimated the upper limits for I p and F p focusing on the flare associated with the strongest ground level enhancement (GLE) directly observed to date (GLE 05 on 23 February 1956), and that inferred for the cosmogenic radionuclide-based SEP event of AD774/775. Results. A scaling law relating I p and F p to the solar soft X-ray peak intensity (F SXR ) as ∝ F 5/6 SXR for a flare with a F SXR = X600 (in the revised scale) is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775.

Athanasios Papaioannou↗

NASA NTRS1976

Effects of forward velocity on turbulent jet mixing noise

Flight simulation experiments were conducted in an anechoic free jet facility over a broad range of model and free jet velocities. The resulting scaling laws were in close agreement with scaling laws derived from theoretical and semiempirical considerations. Additionally, measurements of the flow structure of jets were made in a wind tunnel by using a laser velocimeter. These tests were conducted to describe the effects of velocity ratio and jet exit Mach number on the development of a jet in a coflowing stream. These turbulence measurements and a simplified Lighthill radiation model were used in predicting the variation in radiated noise at 90 deg to the jet axis with velocity ratio. Finally, the influence of forward motion on flow-acoustic interactions was examined through a reinterpretation of the 'static' numerical solutions to the Lilley equation.

Plumblee, H. E., Jr.↗

NASA NTRS1985

Verification of large space structures using scale modelling laws

The feasibility of testing large space structures in 1-g environment for the purpose of verifying its performance requirement is considered. Because of the difference in test objectives as compared to the conventional structural systems, the scale modelling laws are examined. The investigation is performed on a generic structural element, a space beam. A preliminary conclusion is obtained based on the results.

Chen, J.-C.↗

NASA NTRS1982

Model helicopter rotor low frequency broadband noise

The results of an experimental investigation of low frequency broadband noise (LFBN) radiated from model helicopter rotors are presented. The results up to tip Mach number of 0.50 suggest that the peak sound pressure level (SPL) of LFBN appears to follow tip Mach number to a fourth power law and rms velocity of turbulence to a second power law. The experimental results on the effect of tip speed and advance ratio on the peak SPL of LFBN can be explained on the basis of a simple scaling law. However, the experimental results on the effect of blade loading on the peak SPL of LFBN is still not clearly understood. A simple peak SPL scaling law for noise from a helicopter in forward flight encountering a sinusoidal gust is also developed. The trends predicted by the scaling law with the experimental results are found satisfactory for the cases of variation of the peak SPL of LFBN with tip speed and advance ratio.

Humbad, N. G.↗

NASA NTRS2005

Scaling the Non-linear Impact Response of Flat and Curved Composite Panels

The application of scaling laws to thin flat and curved composite panels exhibiting nonlinear response when subjected to low-velocity transverse impact is investigated. Previous research has shown that the elastic impact response of structural configurations exhibiting geometrically linear response can be effectively scaled. In the present paper, a preliminary experimental study is presented to assess the applicability of the scaling laws to structural configurations exhibiting geometrically nonlinear deformations. The effect of damage on the scalability of the structural response characteristics, and the effect of scale on damage development are also investigated. Damage is evaluated using conventional methods including C-scan, specimen de-plying and visual inspection of the impacted panels. Coefficient of restitution and normalized contact duration are also used to assess the extent of damage. The results confirm the validity of the scaling parameters for elastic impacts. However, for the panels considered in the study, the extent and manifestation of damage do not scale according to the scaling laws. Furthermore, the results indicate that even though the damage does not scale, the overall panel response characteristics, as indicated by contact force profiles, do scale for some levels of damage.

Ambur, Damodar R.↗

NASA NTRS2017

Robotically Assembled Aerospace Structures: Digital Material Assembly using a Gantry-Type Assembler

This paper evaluates the development of automated assembly techniques for discrete lattice structures using a multi-axis gantry type CNC machine. These lattices are made of discrete components called digital materials. We present the development of a specialized end effector that works in conjunction with the CNC machine to assemble these lattices. With this configuration we are able to place voxels at a rate of 1.5 per minute. The scalability of digital material structures due to the incremental modular assembly is one of its key traits and an important metric of interest. We investigate the build times of a 5x5 beam structure on the scale of 1 meter (325 parts), 10 meters (3,250 parts), and 30 meters (9,750 parts). Utilizing the current configuration with a single end effector, performing serial assembly with a globally fixed feed station at the edge of the build volume, the build time increases according to a scaling law of n4, where n is the build scale. Build times can be reduced significantly by integrating feed systems into the gantry itself, resulting in a scaling law of n3. A completely serial assembly process will encounter time limitations as build scale increases. Automated assembly for digital materials can assemble high performance structures from discrete parts, and techniques such as built in feed systems, parallelization, and optimization of the fastening process will yield much higher throughput.

Mechanical Structure↗

NASA NTRS2017

Robotically Assembled Aerospace Structures: Digital Material Assembly using a Gantry-Type Assembler

This paper evaluates the development of automated assembly techniques for discrete lattice structures using a multi-axis gantry type CNC machine. These lattices are made of discrete components called "digital materials." We present the development of a specialized end effector that works in conjunction with the CNC machine to assemble these lattices. With this configuration we are able to place voxels at a rate of 1.5 per minute. The scalability of digital material structures due to the incremental modular assembly is one of its key traits and an important metric of interest. We investigate the build times of a 5x5 beam structure on the scale of 1 meter (325 parts), 10 meters (3,250 parts), and 30 meters (9,750 parts). Utilizing the current configuration with a single end effector, performing serial assembly with a globally fixed feed station at the edge of the build volume, the build time increases according to a scaling law of n4, where n is the build scale. Build times can be reduced significantly by integrating feed systems into the gantry itself, resulting in a scaling law of n3. A completely serial assembly process will encounter time limitations as build scale increases. Automated assembly for digital materials can assemble high performance structures from discrete parts, and techniques such as built in feed systems, parallelization, and optimization of the fastening process will yield much higher throughput.

Manufacturing↗

NASA NTRS1992

Composite fuselage shell structures research at NASA Langley Research Center

Fuselage structures for transport aircraft represent a significant percentage of both the weight and the cost of these aircraft primary structures. Composite materials offer the potential for reducing both the weight and the cost of transport fuselage structures, but only limited studies of the response and failure of composite fuselage structures have been conducted for transport aircraft. The behavior of these important primary structures must be understood, and the structural mechanics methodology for analyzing and designing these complex stiffened shell structures must be validated in the laboratory. The effects of local gradients and discontinuities on fuselage shell behavior and the effects of local damage on pressure containment must be thoroughly understood before composite fuselage structures can be used for commercial aircraft. This paper describes the research being conducted and planned at NASA LaRC to help understand the critical behavior or composite fuselage structures and to validate the structural mechanics methodology being developed for stiffened composite fuselage shell structure subjected to combined internal pressure and mechanical loads. Stiffened shell and curved stiffened panel designs are currently being developed and analyzed, and these designs will be fabricated and then tested at Langley to study critical fuselage shell behavior and to validate structural analysis and design methodology. The research includes studies of the effects of combined internal pressure and mechanical loads on nonlinear stiffened panel and shell behavior, the effects of cutouts and other gradient-producing discontinuities on composite shell response, and the effects of local damage on pressure containment and residual strength. Scaling laws are being developed that relate full-scale and subscale behavior of composite fuselage shells. Failure mechanisms are being identified and advanced designs will be developed based on what is learned from early results from the LaRC research activities. Results from combined load tests will be used to validate analytical models of critical nonlinear response mechanisms as well as shell scaling laws.

Starnes, James H., Jr.↗

NASA NTRS1978

Critical phenomena in a low gravity environment

Various types of critical point phenomena are discussed including the gas-liquid phase transition of a fluid, the spontaneous magnetization of a ferromagnet below the Curie temperature, and structural phase transitions of solid materials. The interrelation of thermodynamic properties by scaling laws is considered noting theories for the validity of scaling laws and the principle of universality. Gravity effects are reviewed noting that in earth-based experiments the phenomena are significantly influenced by the earth's gravitational field and that fluid samples that are spatially homogeneous cannot be realized near the gas-liquid critical point.

Sengers, J. V.↗

NASA NTRS1995

The fundamental plane correlations for globular clusters

In the parameter space whose axes include a radius (core, or half-light), a surface brightness (central, or average within the half-light radius), and the central projected velocity dispersion, globular clusters lie on a two-dimensional surface (a plane, if the logarithmic quantities are used). This is analogous to the 'fundamental plane' of elliptical galaxies. The implied bivariate correlations are the best now known for globular clusters. The derived scaling laws for the core properties imply that cluster cores are fully virialized, homologous systems, with a constant (M/L) ratio. The corresponding scaling laws on the half-light scale are differrent, but are nearly identical to those derived from the 'fundamental plane' of ellipticals. This may be due to the range of cluster concentrations, which are correlated with other parameters. A similar explanation for elliptical galaxies may be viable. These correlations provide new empirical constraints for models of globular cluster formation and evolution, and may also be usable as rough distance-indicator relations for globular clusters.

Djorgovski, S.↗