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Results for “Analytic linearization”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Large deflection, large amplitude vibrations and random response of symmetrically laminated rectangular plates

An analytical method is presented for determining large-deflection static bending, large-amplitude free and forced vibrations, and large-amplitude random response of a clamped, symmetrically laminated, rectangular, thin plate subjected to a uniformly distributed transverse loading. Both movable and immovable inplane boundary conditions are considered. Numerical results for bending deflections and strains, frequency ratios, mean-square center deflections and mean-square maximum strains are presented showing the parametric effects of plate length-to-width ratio, orientation of layers, and intensities of applied force for both the linear and nonlinear cases. The analytical results for large-deflection random response are verified through comparison with experimental data.

Gray, C. E., Jr.↗
NASA NTRS1988

The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.

Ng, C. F.↗
NASA NTRS1981

A model for the acoustic impedance of linear suppressor materials bonded on perforated plate

An analytical model is developed for the acoustic impedance of a composite made of a fine screen bonded to a perforated plate, the resistance having been modeled using steady flow theory and data, and including both linear and nonlinear components. The model of the screen resistance alone is derived first, and it is then extended to include a perforated plate bonded to the screen. Quantities such as effective open ratio and pressure recovery are evaluated. Conclusions are presented, including: (1) when the screen is bonded to a perforated plate, the linear resistance increases as the inverse of the perforate open area, (2) the nonlinearity in the screen resistance depends on the square of the screen wire diameter, and (3) when the resistance is considered as a function of approach velocity, the screen nonlinear term increases as the inverse of the square of the perforated plate open area ratio. The general theory can be applied to any screen structure, but final results are limited to a twilled square weave screen. Results can be applied to the study of sound absorbing materials used for lining the walls of aircraft engine duct suppressors.

Rice, E. J.↗
NASA NTRS1959

The Synthesis of Optimum Homing Missile Guidance Systems with Statistical Inputs

An analytical approach is presented which is applicable to the optimization of homing navigation guidance systems which are forced to operate in the presence of radar noise. The two primary objectives are to establish theoretical minimum miss distance performance and a method of synthesizing the optimum control system. The factors considered are: (1) target evasive maneuver, (2) radar glint noise, (3) missile maneuverability, and (4) the inherent time-varying character of the kinematics. Two aspects of the problem are considered. In the first, consideration is given only to minimization of the miss distance. The solution given cannot be achieved in practice because the required accelerations are too large. In the second, results are extended to the practical case where the limited acceleration capabilities of the missile are considered by placing a realistic restriction on the mean-square acceleration so that system operation is confined to the linear range. Although the exact analytical solution of the latter problem does not appear feasible, approximate solutions utilizing time-varying control systems can be found. One of these solutions - a range multiplication type control system - is studied in detail. It is shown that the minimum obtainable miss distance with a realistic restriction on acceleration is close to the absolute minimum for unlimited missile maneuverability. Furthermore, it is shown that there is an equivalence in performance between the homing and beam-rider type guidance systems. Consideration is given to the effect of changes in target acceleration, noise magnitude, and missile acceleration on the minimum miss distance.

Stewart, Elwood C.↗
NASA NTRS1979

Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques

Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers.

Lehtinen, B.↗
NASA NTRS1981

Analytical performance prediction for large antennas

A linear mathematical modeling of the static and dynamic characteristics of a deployable offset wrap rib antenna was attempted using small motions in an effort to simulate the surface distortion resulting from thermal loading and transient oscillations from control. Both cyclic symmetry and model synthesis were used for parametric analysis. Although the ribs can be modeled as slender beams varying cross sections and equivalent linear material properties, the mesh poses a problem since its equivalent stress strain relations are highly nonlinear and sensitive to the biaxial prestressed state. Consequently, the macroscopic material properties were measured experimentally in the neighborhood of the design prestress. An equivalent tangent modulus technique was then adopted about this equilibrium state and assumed to be valid within a small range of incremental stresses.

El-Raheb, M.↗
NASA NTRS1990

Inhomogeneous electric field effects in a linear RF quadruple trap

The exact potential corresponding to confining fields inside a linear rf quadrupole particle trap of finite length is presented. The analytic expressions for the trapping potential is derived by introducing a linear trap employing a relatively simple cylindrical geometry and solving Laplace's equation for the trap electrodes. The finite length of linear traps results in field distortion near the trap ends. An exact analytic determination of the fields is useful because the profile of the trapped ion cloud is highly dependent on the fields confining it. It is shown that near the ends of the trap, the effective potential arising from the rf fields acts to propel particles out of the trap, and further, that the addition of a dc bias generates an inhomogeneous in the trap that influences the particles both perpendicularly to and along the trap's long axis.

Melborne, R. K.↗
DOE OSTI2024

Robust Data-Driven Predictive Run-to-Run Control for Automated Serial Sectioning

This letter presents a one-step predictive run-to-run controller (R2R-MPC) for the automation of mechanical serial sectioning (MSS), a destructive material analysis process. To address the inherent uncertainty and disturbances in the MSS process, a robust closed-loop approach is presented. Here, the robust R2R-MPC models the uncertainty of the MSS process using a linear differential inclusion. As an analytical model of the MSS process is unavailable, the differential inclusion is identified from historical data. The R2R-MPC is posed as an optimization problem that computes incremental changes to the control input which minimize the worst-case material removal errors. This optimization-based controller is combined with a run-to-run controller to provide integral action that rejects constant disturbances and tracks constant reference removal rates. To demonstrate the efficacy of our robust R2R-MPC, we present simulation results which compare the presented controller with a conventional non-robust R2R.

42 ENGINEERING↗
DOE OSTI2024

Modifying the Asynchronous Jacobi Method for Data Corruption Resilience

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge computing environments can operate on data in situ, offering enticing benefits over data aggregation to HPC and CC facilities that include avoiding costs of transmission, increased data privacy, and real-time data analysis. Because of the inherent unreliability of edge computing environments, new fault-tolerant approaches must be developed before the benefits of edge computing can be realized. Motivated by algorithm-based fault tolerance, a variant of the asynchronous Jacobi (ASJ) method is developed that achieves resilience to data corruption by rejecting solution approximations from neighbor devices according to a bound derived from convergence theory. Numerical results on a two-dimensional Poisson problem show that the new rejection criterion, along with a novel approximation to the shortest path length on which the criterion depends, restores convergence for the ASJ variant in the presence of certain types data corruption. Numerical results are obtained for when the singular values in the analytic bound are approximated. Additional linear systems are also explored, one with a more dense sparsity pattern and one that includes advection. All results indicate that successful resilience to data corruption depends on whether the bound tightens fast enough to reject corrupted data before the iteration evolution deviates significantly from that predicted by the convergence theory defining the bound. This observation generalizes to future work on algorithm-based fault tolerance for other asynchronous algorithms, including upcoming approaches that leverage Krylov subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Heart Shape to Fracture Distance: Characterizing Hydraulic Fracture Propagation before Hits

Estimating the distance from the hydraulic fracture tip to the monitor well can be useful for fracture characterization, well spacing optimization, and preventing parent-child well interference. A heart-shaped signal is referred to as the extensional precursor of a fracture hit recorded by crosswell strain measurements and can serve as a vital tool for such estimation. This study incorporates the 3D displacement discontinuity method (DDM) to understand the impact of fracture geometry and monitor well offset on the heart-shaped signal’s characteristics. Results from numerical simulation and analytical solutions reveal a strong linear correlation between the spatial extent of the heart-shaped signal and the fracture tip distance. This relationship was further developed to predict tip distance using field data from the Hydraulic Fracture Test Site 2 (HFTS2). A reasonable approximation result from field data further validates the methodology. In addition, it is worth noting that the estimation accuracy depends on the ratio between fracture dimension and tip distance. The findings of this study offer a novel approach for real-time monitoring and characterizing hydraulic fracture propagation, which can be further used for well spacing optimization in unconventional and enhanced geothermal system reservoir development, as well as caprock integrity monitoring for carbon sequestration projects.

58 GEOSCIENCES↗
DOE OSTI2024

Characterizing Hydraulic Fracture Propagation Before Fracture Hits

Estimating the distance from hydraulic fracture tip to monitor well can be very useful for fracture characterization, well spacing optimization, and preventing parent-child well interference. Heart-shape signal is referred to as the extensional precursor of fracture hit recorded by cross-well strain measurements and can be served as a vital tool to make such estimation. This study incorporates the 3D Displacement Discontinuity Method to understand the impact of fracture geometry and monitor well offset on the heart-shape signal’s characteristics. Results from numerical simulation and analytical solutions reveal a strong linear correlation between the spatial extent of heart shape signal and fracture tip distance. This relationship was further developed to predict tip distance using field data from the Hydraulic Fracture Test Site 2. A reasonable approximation result from field data further validates the methodology. In addition, it is worth noting that the estimation accuracy depends on the ratio between fracture dimension and tip distance. The findings of this study offer a novel approach for real-time monitoring and characterizing hydraulic fracture propagation, which can be further used for well spacing optimization in unconventional and Enhanced Geothermal System reservoir development, as well as cap rock integrity monitoring for carbon sequestration projects.

Jin, Ge↗
NASA NTRS1971

Analytical and experimental studies of natural vibrations modes of ring-stiffened truncated-cone shells with variable theoretical ring fixity

Experimental and analytical investigations of the vibratory behavior of ring-stiffened truncated-cone shells are described. Vibration tests were conducted on 60 deg conical shells having up to four ring stiffeners and for free-free and clamped-free edge constraints and 9 deg conical shells, for two thicknesses, each with two angle rings and for free-free, free-clamped, and clamped-clamped edge constraints. The analytical method is based on linear thin shell theory, employing the Rayleigh-Ritz method. Discrete rings are represented as composed of one or more segments, each of which is a short truncated-cone shell of uniform thickness. Equations of constraint are used to join a ring and shell along a circumferential line connection. Excellent agreement was obtained for comparisons of experimental and calculated frequencies.

Naumann, E. C.↗
NASA NTRS1971

State estimation with small nonlinearities

A variety of techniques is available for estimating the states of nonlinear dynamic systems from noisy data. The differences among several of these procedures in the presence of small dynamic and observational nonlinearities are investigated. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the others are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. A group of analytic expressions is developed for the mean and covariance of the error in each of these estimators so that they may be compared without lengthy Monte Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points. Under some circumstances, more complicated algorithms can have larger biases than smaller ones.

Conrad, B.↗
NASA NTRS1973

Increasing the sensitivity of the Jaffe reaction for creatinine

Study of analytical procedure has revealed that linearity of creatinine calibration curve can be extended by using 0.03 molar picric acid solution made up in 70 percent ethanol instead of water. Three to five times more creatinine concentration can be encompassed within linear portion of calibration curve.

Tom, H. Y.↗
NASA NTRS1977

Plasma oscillations and Landau damping

The Fourier-Hermite expansion is used to follow the time development of a non-analytic initial perturbation of the linearized Vlasov-Poisson system. The calculations differ from some previous applications of the Fourier-Hermite expansion in that they relax certain symmetry conditions on the distribution functions and in that many coefficients are required to describe the initial conditions. The results confirm Weitzner's prediction of the asymptotic t to the -3rd time dependence for this problem, and exhibit the way in which this behavior develops. An appendix outlines the way in which the initial conditions are expanded in Hermite functions.

Crownfield, F. R., Jr.↗
NASA NTRS1980

Transonic unsteady airloads on an energy efficient transport wing with oscillating control surfaces

An aspect ratio 10.8 supercritical wing with oscillating control surfaces is described. The wing is instrumental with 252 static orifices and 164 in situ dynamic pressure transducers for studying the effects of control surface deflection on steady and unsteady pressures at transonic speeds. Results from initial wind tunnel tests conducted in the Langley Transonic Dynamics Tunnel are discussed. Unsteady pressure results are presented for two trailing edge control surfaces oscillating separately at the design Mach number of 0.78. Some experimental results are compared with analytical results obtained by using linear lifting surface theory.

Sandford, M. C.↗
NASA NTRS1980

Transonic unsteady airloads on an energy efficient transport wing with oscillating control surfaces

An aspect-ratio 10.8 supercritical wing with oscillating control surfaces is described. The wing is instrumented with 252 static orifices and 164 in situ dynamic pressure transducers for studying the effects of control surface deflection on steady and unsteady pressures at transonic speeds. Selected results from initial wind-tunnel tests conducted in the Langley Transonic Dynamics Tunnel are discussed. Unsteady pressure results are presented for two trailing-edge control surfaces oscillating separately at the design Mach number of 0.78. Some experimental results are compared with analytical results obtained by using linear lifting-surface theory.

Sandford, M. C.↗
NASA NTRS1981

An optimization model for energy generation and distribution in a dynamic facility

An analytical model is described using linear programming for the optimum generation and distribution of energy demands among competing energy resources and different economic criteria. The model, which will be used as a general engineering tool in the analysis of the Deep Space Network ground facility, considers several essential decisions for better design and operation. The decisions sought for the particular energy application include: the optimum time to build an assembly of elements, inclusion of a storage medium of some type, and the size or capacity of the elements that will minimize the total life-cycle cost over a given number of years. The model, which is structured in multiple time divisions, employ the decomposition principle for large-size matrices, the branch-and-bound method in mixed-integer programming, and the revised simplex technique for efficient and economic computer use.

Lansing, F. L.↗