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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nosetip, and the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nosetip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the perturbation form of the 2D, harmonic Navier-Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton-Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the GMRES iterative method with a preconditioner corresponding to a simplified Jacobian without the cross derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation (NPSE) results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over the blunt cone. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher frequency Mack’s second-mode instabilities further downstream.

boundary layer transition↗
NASA NTRSDate not supplied

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nosetip, and the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nosetip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the perturbation form of the 2D, harmonic Navier-Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton-Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the GMRES iterative method with a preconditioner corresponding to a simplified Jacobian without the cross derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation (NPSE) results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over the blunt cone. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher frequency Mack’s second-mode instabilities further downstream.

boundary layer transition↗
NASA NTRS1975

Application of the comparison principle to analysis of nonlinear systems

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Gunderson, R. W.↗
NASA NTRS1985

An Integrated Analysis of the Physiological Effects of Space Flight: Executive Summary

A large array of models were applied in a unified manner to solve problems in space flight physiology. Mathematical simulation was used as an alternative way of looking at physiological systems and maximizing the yield from previous space flight experiments. A medical data analysis system was created which consist of an automated data base, a computerized biostatistical and data analysis system, and a set of simulation models of physiological systems. Five basic models were employed: (1) a pulsatile cardiovascular model; (2) a respiratory model; (3) a thermoregulatory model; (4) a circulatory, fluid, and electrolyte balance model; and (5) an erythropoiesis regulatory model. Algorithms were provided to perform routine statistical tests, multivariate analysis, nonlinear regression analysis, and autocorrelation analysis. Special purpose programs were prepared for rank correlation, factor analysis, and the integration of the metabolic balance data.

Leonard, J. I.↗
NASA NTRS1992

Program Solves Euler Equations Of Supersonic Flow

EMTAC (Euler Marching Technique For Accurate Computation) computer program employs Euler marching algorithm for computing supersonic flows. Enables accurate nonlinear analysis of nonlinear dynamics of supersonic flow over wide range of supersonic mach numbers and angles of attack. Based on exact equations of dynamics of inviscid gas and valid for computations of flows at low and high supersonic mach numbers exhibiting strong shocks and rotational effects. Program also used for inviscid three-dimensional flows fully subsonic or transonic (subsonic with supersonic pockets). Written in FORTRAN V.

Szema, Kuo-Yen↗
NASA NTRS1961

Study of Systems Using Inertia Wheels for Precise Attitude Control of a Satellite

Systems using inertia wheels are evaluated in this report to determine their suitability for precise attitude control of a satellite and to select superior system configurations. Various possible inertia wheel system configurations are first discussed in a general manner. Three of these systems which appear more promising than the others are analyzed in detail, using the Orbiting Astronomical Observatory as an example. The three systems differ from each other only by the method of damping, which is provided by either a rate gyro, an error-rate network, or a tachometer in series with a high-pass filter. An analytical investigation which consists of a generalized linear analysis, a nonlinear analysis using the switching-time method, and an analog computer study shows that all three systems are theoretically capable of producing adequate response and also of maintaining the required pointing accuracy for the Orbiting Astronomical Observatory of plus or minus 0.1 second of arc. Practical considerations and an experimental investigation show, however, that the system which uses an error-rate network to provide damping is superior to the other two systems. The system which uses a rate gyro is shown to be inferior because the threshold level causes a significant amount of limit-cycle operation, and the system which uses a tachometer with a filter is shown to be inferior because a device with the required dynamic range of operation does not appear to be available. The experimental laboratory apparatus used to investigate the dynamic performance of the systems is described, and experimental results are included to show that under laboratory conditions with relatively large extraneous disturbances, a dynamic tracking error of less than plus or minus 0.5 second of arc was obtained.

White, John S.↗
NASA NTRS1986

Nonlinear rotordynamics analysis

Three analytic consequences of the nonlinear Jeffcott equations are examined. The primary application of these analyses is directed toward understanding the excessive vibrations recorded in the Liquid Oxygen (LOX) pump of the Space Shuttle Main Engine (SSME) during hot firing ground testing. The first task is to provide bounds on the coefficients of the equations which delimit the two cases of numerical solution as a circle or an annulus. The second task examines the mathematical generalization to multiple forcing functions, which includes the special problems of mass imbalance, side force, rubbing, and combination of these forces. Finally, stability and boundedness of the steady-state solutions is discussed and related to the corresponding linear problem.

Day, W. B.↗
NASA NTRS2007

Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts

Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.

Sreekantamurthy, Tham↗
NASA NTRS1993

Develop advanced nonlinear signal analysis topographical mapping system

This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate feasible engineering solutions. The final result of this program will yield an advanced nonlinear signal analysis topographical mapping system (ATMS) of nonlinear and nonstationary spectral analysis software package integrated with the Compressed SSME TOPO Data Base (CSTDB) on the same platform. This system will allow NASA engineers to retrieve any unique defect signatures and trends associated with different failure modes and anomalous phenomena over the entire SSME test history across turbopump families.

Jong, Jen-Yi↗
NASA NTRS1987

Nonlinear dynamic analysis of quasi-symmetric anisotropic structures

An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.

Noor, Ahmed K.↗
NASA NTRS1988

Analysis of nonlinear internal waves in the New York Bight

An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX). The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions. The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets. From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons.

Liu, Antony K.↗
NASA NTRS1987

Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.

Cardoso, J. B.↗
NASA NTRS1993

Hybrid Analytical Technique for Nonlinear Vibration Analysis of Thin-Walled Beams

A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.

Noor, Ahmed K.↗
NASA NTRS1982

Large displacements and stability analysis of nonlinear propeller structures

The use of linear rigid formats in COSMIC NASTRAN without DMAP procedures for the analysis of nonlinear propeller structures is described. Approaches for updating geometry and applying follower forces for incremental loading are demonstrated. Comparisons are made with COSMIC NASTRAN rigid formats and other independent finite element programs. Specifically, the comparisons include results from the four approaches for updating the geometry using RIGID FORMAT 1, RIGID FORMATS 4 and 13, MARC and MSC/NASTRAN. It is shown that 'user friendly' updating approaches (without DMAPS) can be used to predict the large displacements and instability of these nonlinear structures. These user friendly approaches can be easily implemented by the user and predict conservative results.

Aiello, R. A.↗
NASA NTRS1982

Large displacements and stability analysis of nonlinear propeller structures

The use of linear rigid formats in COSMIC NASTRAN without DMAP procedures for the analysis of nonlinear propeller structures is described. Approaches for updating geometry and applying follower forces for incremental loading are demonstrated. The COSMIC NASTRAN rigid formats and other independent finite element programs are compared. The comparisons include results from the four approaches for updating the geometry using RIGID FORMAT 1, RIGID FORMATS 4 and 13, MARC and MSC/NASTRAN. It is shown that user friendly updating approaches can be used to predict the large displacements and instability of these nonlinear structures. The approaches are easily implemented by the user and predict conservative results.

Aiello, R. A.↗
NASA NTRS1990

Theoretical hypervelocity ballistic limit for single or double plates using nonlinear modal analysis

The original research on the use on nonlinear vibration technique to solve for the hypervelocity ballistic limit for double plates is examined. Such structure is commonly found in typical Space Station design where the incoming space or man-made debris would be fragmented upon hitting the outer plate (shield) and the subsequent impact on the main wall would result in a much reduced damge of the space station or spacecraft. The existing few theoretical impact equations do not agree well with each other. The existing computer code bumper used at NASA-Johnson Space Center appears to predict an unconservative ballistic limit when compared with experimental data where the velocity ranges from 3 km/s to 8 km/s. Such unconservative prediction is unacceptable from a practical safe design point of view. The bumper code is based on Wilkinson's (1968) paper and his equations have not been improved nor modified even though they are viewed with suspicion due to lack of agreement with experiments. To make matters worse, there is not another theory which is better than Wilkinson's equation and the designers are forced to use purely empirical Nysmith (1969) or semiempirical equations developed by Cour-Palais in 1969. The Cour-Palais equations were later modified empirically in 1989. The purpose of the present investigation is to examine the many assumptions of the Wilkinson equation. An attempt is made to present design charts based on the modified-Wilkinson equation so that the designer can get a feel of the ranges of the parameters which are of interest and discard a huge range of parameters, thus, significantly reducing the number of test shots required. The analysis is based on a solution of the governing nonlinear differential equations for a plate, assuming axisymmetric behavior using polar coordinates.

Hui, David↗