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At least 109 records · Page 6

Correlation of finite element free vibration predictions using random vibration test data

Finite element analysis is regularly used during the engineering cycle of mechanical systems to predict the response to static, thermal, and dynamic loads. The finite element model (FEM) used to represent the system is often correlated with physical test results to determine the validity of analytical results provided. Results from dynamic testing provide one means for performing this correlation. One of the most common methods of measuring accuracy is by classical modal testing, whereby vibratory mode shapes are compared to mode shapes provided by finite element analysis. The degree of correlation between the test and analytical mode shapes can be shown mathematically using the cross orthogonality check. A great deal of time and effort can be exhausted in generating the set of test acquired mode shapes needed for the cross orthogonality check. In most situations response data from vibration tests are digitally processed to generate the mode shapes from a combination of modal parameters, forcing functions, and recorded response data. An alternate method is proposed in which the same correlation of analytical and test acquired mode shapes can be achieved without conducting the modal survey. Instead a procedure is detailed in which a minimum of test information, specifically the acceleration response data from a random vibration test, is used to generate a set of equivalent local accelerations to be applied to the reduced analytical model at discrete points corresponding to the test measurement locations. The static solution of the analytical model then produces a set of deformations that once normalized can be used to represent the test acquired mode shapes in the cross orthogonality relation. The method proposed has been shown to provide accurate results for both a simple analytical model as well as a complex space flight structure.

Chambers, Jeffrey A.↗

Effects of confinement on partially premixed flames

Partially premixed combustion is an intermediate regime between the limiting cases of premixed and nonpremixed combustion. Although combustion problems are generally approached from one of these two limiting cases, there are many practical situations where flames cannot be considered as purely premixed or nonpremixed, and thus the partially premixed approach must be used. In partially premixed combustion, mechanisms from the premixed and nonpremixed regimes can coexist, and as a result some interesting new phenomena can arise. One such phenomenon is the flame stabilization in laminar mixing layers by triple flames. One of the first observations of triple flames was made by Phillips (1965), who investigated a triple flame propagating in a methane mixing layer. Kioni et al. (1993) also examined triple flames both experimentally and numerically. There have also been numerous analytical studies on the shape and propagation of triple flames under various assumptions by Dold (1989), Dold et al. (1991), and Hartley and Dold (1991). In terms of modeling, Muller et al. (1994) have combined the flamelet formulations for premixed and nonpremixed combustion in order to treat lifted diffusion flames. One common feature in the analytical and numerical studies mentioned above is the assumption of zero heat release, which is necessary to make the problem tractable. The effect of heat release on triple flames was investigated by Ruetsch et al. (1995), where for the unconfined case, flame speeds larger than their premixed counterparts were found. One of the most important practical situations in which these conditions arise is in lifted turbulent jet diffusion flames. At a critical velocity the burning zone of a fuel jet lifts off from the nozzle, moves to increasing distances as the jet velocity increases, and finally blows off. The mechanisms that control these phenomena, i.e. that determine the stability of these flames, are still not understood. In addition to regions where diffusion flame stabilization takes place, partially premixed conditions also exist during the ignition process in nonpremixed systems. Numerical simulations by Reveillon et al. (1994) of the ignition process in a weakly stirred mixture of fuel and oxidizer show that triple flames propagate along lines of stoichiometric mixture fraction throughout the fluid. In addition, Peters (1994) notes that NO(x) emissions are likely to be large in such transient cases, and therefore an understanding of triple flames can provide information concerning pollutant formation. This study extends the work previously done and examines the effects of lateral confinement on partially premixed flames. Once again, we study both the flame structure and propagation.

Ruetsch, G. R.↗

Free vibrations of delaminated beams

Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. A generalized vibrational principle is used to formulate the equation of motion and associated boundary conditions for the free vibration of a composite beam with a delamination of arbitrary size and location. The effect of coupling between longitudinal vibration and bending vibration is considered. This coupling effect is shown to significantly affect the calculated natural frequencies and mode shapes of the delaminated beam.

Shen, M.-H. H.↗

Growth Angle: A Microscopic View

A microscopic continuum mechanical model of the growth angle is proposed. It is based on the van der Waals type framework that is used for surface force phenomena. The obtained augmented Laplace type integro-differential equations are, in general, difficult to analyze. Here we focused primarily on the particular case of equal melt and crystal surface energies. We derived an approximate equation for the meniscus shape, and obtained an analytical relationship between the contact and the growth angle. Interestingly, the same result can be obtained using the macroscopic model of Herring. The case of a macroscopically sharp corner is also considered. For this case, the macroscopic angle is not defined and it can be any angle between the contact angles of both flat surfaces. The microscopic model yields the smooth shape for the meniscus that also is not unique, but depends on the initial position of the meniscus.

Mazuruk, Konstantin↗

An analytical procedure for computing smooth transitions between two specified cross sections with applications to blended wing body configuration

An analytical procedure is described for designing smooth transition surfaces for blended wing-body configurations. Starting from two specified cross section shapes, the procedure generates a gradual transition from one cross section shape to the other as an analytic blend of the two shapes. The method utilizes a conformal mapping, with subsequent translation and scaling, to transform the specified and shapes to curves that can be combined more smoothly. A sample calculation is applied to a blended wing-body missile type configuration with a top mounted inlet.

Barger, R. L.↗

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Kane, James H.↗

Free vibrations of delaminated beams

Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.

Shen, M.-H. H.↗

Capturing, Analyzing, Maintaining, and Disseminating Shape Memory Material Data Between Information Management Systems

With an increased demand on reducing the time, cost, and effort to develop new materials, Integrated Computational Materials Engineering (ICME) has received widespread attention in various engineering disciplines as a catalyst for significantly reducing experimental testing during the material design process. An ICME approach to design can enable ‘fit-for-purpose’ materials to be realized in engineering applications by incorporating well-understood process-property-performance relationships between the various length and time scales in a material’s structure, enabling material optimization. However, such an approach requires validated multiscale models at the various length scales for a material, which in turn requires a large amount of data, a robust means of storing the data, and the ability to link data to developed material models. The NASA Vision 2040 [1] has identified nine key elements to enabling ICME approaches in system level design, with one being “Data, Information, and Visualization”, thus outlining the importance of a robust information management system for ICME. As the relationship between microstructure, properties, and material performance become better understood and incorporated into multiscale models that can be leveraged in application design, the emergence of new materials with application-driven properties can be realized. One such new material class that has seen growing attention are shape memory materials (SMM), in which a material can transition between a deformed and undeformed state via a reversible phase transformation when subject to a thermal, mechanical, or magnetic load [2]. SMMs have been used widely in aerospace and biomedical industries, including applications such as actuators, low-shock mechanisms, medical staples, braces, and stents [3, 4]. These materials exhibit unique behavior due to their ability to transition between phases, and thus the mechanisms that enable this transition must be captured in a data information management system and incorporated into SMM material models. At NASA Glenn Research Center, the Shape Memory Materials Database (SMMD) Tool has been developed to capture the necessary information that governs SMM material behavior and provide users the ability to select and visualize various SMMs for a specific application [5]. The database contains point-wise data for published SMM materials, along with the pedigree metadata for traceability necessary for a robust information management system. The database is also capable of storing in-house test data performed at NASA GRC by interacting with the developed Shape Memory Alloy (SMA) Analytics tool to extract the necessary point-wise values and populate the database. Although the SMMD Tool offers its users a single, authoritative source for SMM material data that is critical for model development and material design, the full material pedigree of the in-house test data for SMMs is not currently captured and is out of the scope for the SMMD tool. In this work, the schema for capturing SMM test data within the larger NASA GRC ICME Schema [6, 7, 8, 9] will be developed and implemented for thermomechanical tests conducted at NASA GRC. The developed schema will not only store the relevant data needed for the SMMD tool, but also the material pedigree (i.e., production of the bulk material, bulk material analysis, sample cut-out diagrams, sample fabrication procedure, etc.), test pedigree (i.e., test equipment used, measurement systems used, raw test data), and analysis pedigree (i.e., how the data in the SMMD tool is calculated). Furthermore, a Python-based framework will be developed to seamlessly interact between the SMA Analytics and SMMD tools, which will write the full dataset and associated metadata to the GRC Information Management System before passing the required point-wise data to the SMMD tool. Data informatics is a key element of the NASA Vision 2040, which requires not only that data is stored and maintained throughout the material lifecycle, but that the data is also accessible and reusable such that material development efforts can be minimized. Therefore, for an ICME design approach to be realized, a centralized information management system that drives the ICME process must be able to communicate with other databases. The work that will be presented in this presentation will therefore not only demonstrate the ability of NASA GRC’s information management system to capture SMM data, but also its ability to interact with pre-existing tools specialized for such materials.

Data management↗

The effect of sensor and actuator errors on static shape control for large space structures

An analytical study was performed to predict and assess the effect of actuator and sensor errors on the performance of a shape control procedure for flexible space structures using applied temperatures. Approximate formulas were derived for the expected value and variance of the rms distortion ratio (ratio of rms distortions with and without corrections) based on the assumption of zero-mean normally distributed random errors in measured distortions and actuator output temperatures. Studies were carried out for a 55-meter radiometer antenna reflector distorted from its ideal parabolic shape by nonuniform orbital heating. The first study consisted of varying the sensor and actuator errors for the case of 12 actuators and computing the distortion ratio. In the second study, sensor and actuator errors were prescribed and the effect of increasing the number of actuators was evaluated.

Haftka, R. T.↗

Effect of sensor and actuator errors on static shape control for large space structures

An analytical study was performed to predict and assess the effect of actuator and sensor errors on the performance of a shape control procedure for flexible space structures using applied temperatures. Approximate formulas were derived for the expected value and variance of the rms distortion ratio (ratio of rms distortions with and without corrections) based on the assumption of zero-mean normally distributed random errors in measured distortions and actuator output temperatures. Studies were carried out for a 55-meter radiometer antenna reflector distorted from its ideal parabolic shape by nonuniform orbital heating. The first study consisted of varying the sensor and actuator errors for the case of 12 actuators and computing the distortion ratio. In the second study, sensor and actuator errors were prescribed and the effect of increasing the number of actuators was evaluated.

Haftka, Raphael T.↗

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

CODEX weak lensing mass catalogue and implications on the mass–richness relation

The COnstrain Dark Energy with X-ray clusters (CODEX) sample contains the largest flux limited sample of X-ray clusters at 0.35 < z < 0.65. It was selected from ROSAT data in the 10 000 square degrees of overlap with BOSS, mapping a total number of 2770 high-z galaxy clusters. We present here the full results of the CFHT CODEX programme on cluster mass measurement, including a reanalysis of CFHTLS Wide data, with 25 individual lensing-constrained cluster masses. We employ lensfit shape measurement and perform a conservative colour–space selection and weighting of background galaxies. Using the combination of shape noise and an analytic covariance for intrinsic variations of cluster profiles at fixed mass due to large-scale structure, miscentring, and variations in concentration and ellipticity, we determine the likelihood of the observed shear signal as a function of true mass for each cluster. We combine 25 individual cluster mass likelihoods in a Bayesian hierarchical scheme with the inclusion of optical and X-ray selection functions to derive constraints on the slope α, normalization β, and scatter σln λ|μ of our richness–mass scaling relation model in log-space: ${\langle {\rm In}\,\, \lambda\!\!\mid\!\!\mu\rangle = \alpha\mu + \beta,} $ with μ = ln (M 200c /M piv ), and M piv = 10 14.81 M ⊙ . We find a slope $\alpha = 0.49^{+0.20}_{-0.15}$, normalization $\exp (\beta) = 84.0^{+9.2}_{-14.8}$, and $\sigma _{\ln \lambda | \mu } = 0.17^{+0.13}_{-0.09}$ using CFHT richness estimates. In comparison to other weak lensing richness–mass relations, we find the normalization of the richness statistically agreeing with the normalization of other scaling relations from a broad redshift range (0.0 < z < 0.65) and with different cluster selection (X-ray, Sunyaev–Zeldovich, and optical).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Unraveling Fano noise and the partial-charge-collection effect in x-ray spectra below 1 keV

Fano noise, readout noise, and the partial-charge-collection (PCC) effect collectively contribute to the degradation of energy spectra in charge-coupled device (CCD) measurements, especially at low energies. Here, in this work, the x rays produced by the fluorescence of fluorine (677 eV) and aluminum (1486 eV) were recorded using a Skipper-CCD, which enabled the readout noise to be reduced to 0.2 e - . Based on an analytical description of photopeak shapes resulting from the convolution of the PCC effect and Fano noise, we achieved a precise characterization of the energy spectra. This description enabled us to disentangle and quantify the contributions from both Fano noise and the PCC effect. As a result, we determined the Fano factor and the electron-hole pair creation energy. Additionally, we estimated the PCC region of the sensor and, for the first time, experimentally observed the expected skewness of photopeaks at low energies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Density and flux distributions in the lunar atmosphere due to point and line sources

Apart from the globally distributed ambient gases in the lunar atmosphere, localized gas sources, such as volcanos, may have a measurable effect on the process of shaping the lunar atmosphere. Analytic solutions were obtained for the spatial distributions of neutral gas densities and fluxes due to point and line sources at the lunar surface. Both density and flux profiles are strong functions of the distance from the source to the point of observation. The study also reveals that: (1) The location of the source may be identified from the density and flux profiles. (2) If the gas species is known, the temperature of the gas may be determined from the density gradient at a distance of several scale heights from the source. (3) The strength of the gas source may be determined by the magnitudes of density and flux.

Yeh, T. T. J.↗

Blade selection for a modern axial-flow compressor

The procedures leading to successful design of an axial flow compressor are discussed. The three related approaches to cascade selection are: (1) experimental approach which relies on the use of experimental results from identical cascades to satisfy the velocity diagrams calculated, (2) a purely analytical procedure whereby blade shapes are calculated from the theoretical cascade and viscous flow equations, and (3) a semiempirical procedure which used experimental data together with the theoretically derived functional relations to relate the cascade parameters. Diagrams of typical transonic blade sections with uncambered leading edges are presented.

Wright, L. C.↗

Kp dependence of the plasma sheet boundary

An empirical relationship has been obtained between the location of the inner boundary of the plasma sheet along the geostationary orbit and Kp. Through the use of an analytical expression for the shape of the boundary and a relationship between the convection electric field and Kp this result is extended to yield the radial position of the boundary versus Kp. The result illustrates the high degree of sensitivity of measurements in the geostationary orbit region to shifts in the plasma sheet position arising from geomagnetic activity or an increasing convection electric field.

Freeman, J. W.↗

Application of a numerical orthogonal coordinate generator to axisymmetric blunt bodies

An application of a simple numerical technique which allows for the rapid construction of orthogonal coordinate systems about axisymmetric blunt bodies is presented. This technique can generate orthogonal meshes which have unequally spaced points in two directions. Relations are given for the numerical generation of the metric coefficients. Body shapes ranging from simple analytical bodies to complex reverse curvature bodies are presented together with their orthogonal coordinate systems. The relatively good accuracy of the technique is shown in tabular data describing coordinate line slopes and metric coefficients. The predictor-corrector numerical method used to generate these results is both simple in concept and easy to program, so that the application of the technique should be broader than the results presented.

Graves, R. A., Jr.↗