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At least 55 records · Page 3

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Wundrow, David W.↗

Coupled rotor-fuselage vibration reduction with multiple frequency blade pitch control

A nonlinear coupled rotor/flexible fuselage analysis has been developed and used to study the effects of higher harmonic blade pitch control on the vibratory hub loads and fuselage acceleration levels. Previous results, obtained with this model have shown that conventional higher harmonic control (HHC) inputs aimed at hub shear reduction cause an increase in the fuselage accelerations and vice-versa. It was also found that for simultaneous reduction of hub shears and fuselage accelerations, a pitch input representing a combination of two higher harmonic components of different frequencies was needed. Subsequently, it was found that this input could not be implemented through a conventional swashplate. This paper corrects a mistake originally made in the representation of the multiple frequency pitch input and shows that such a pitch input can be only implemented in the rotating reference frame. A rigorous mathematical solution is found, for the pitch input in the rotating reference frame, which produces simultaneous reduction of hub shears and fuselage acceleration. New insight on vibration reduction in coupled rotor/fuselage systems is obtained from the sensitivity of hub shears to the frequency and amplitude of the open loop HHC signal in the rotating reference frame. Finally the role of fuselage flexibility in this class of problems is determined.

Papavassiliou, I.↗

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Karney, C. F. F.↗

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Brenner, Martin J.↗

A comparison of experimental observations and numerical predictions for the initiation of fiber microbuckling in notched composite laminates

The results of the present experimental study of fiber microbuckling indicates that free surfaces, ply orientations, and resin-rich regions affect the strain level for the initiation of in-plane fiber microbuckling. Nonlinear matrix constitutive behavior, in conjunction with initial fiber waviness, cause significant reductions of fiber microbuckling initiation strain level; these two factors generate nonlinear global stress-strain responses in the models. The fiber microbuckling initiation strains correlate well with the applied strain associated with asymptotic local shear strains.

Guynn, E. G.↗

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗

Finite element modeling and analysis of tires

Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.

Noor, A. K.↗

Modeling Whitecaps on Global Scale

Whitecaps play an important role in the surface-atmosphere interactions across the ocean. They are directly linked to the energy dissipation rate during wave breaking and transfer of heat, momentum, and gas/aerosol exchange from the wind to the sea surface. Although the first models of W were dependent only on wind speeds, a large number of diverse models based on wind and sea state which include wave height, wave age, friction velocity, and stability effects have been proposed since then. However, it is recognized that most of the proposed W models have strong systematic (e.g., zonal bias) and random errors when compared against observations. This is partly due to the differences in environmental conditions, measurement techniques, and geographical locations among these studies. But, some of these biases are linked to the inability of the proposed models to capture the variability in W in certain wind/wave regimes. Despite the knowledge of existing biases, W residual relationships from the models with wind and wave fields remain highly uncertain, with residual trends varying between the published studies. Here, we take advantage of the availability of relatively dense observations of W from WindSat microwave satellite retrievals in combination with the University of Miami wave model which was recently incorporated within the NASA GMAO/GEOS system (GEOS-UMWM). We use Windsat W retrievals to assess and constrain the previously published W models and understand the relationships of residuals from models in different wind/wave regimes. We link these unexplained residual variations to additional factors such as swell index, drag coefficient etc and add information to the existing whitecap models. Since Windsat retrievals cover wide range of environmental conditions, it helps to reduce the uncertainties associated with differences in measurement techniques. Regression of wind-wave fields against all Windsat data points (CTL) results in larger residuals for lower wave age and W is overestimated upto ~4% for wave age < 10 and underestimated by upto ~2% as wave age increases. We attest to this bias by considering two approaches. One is to perform regression separately for different stages of wave development such as developing sea, fully developed, and wind sea regimes thereby understanding the sensitivity of regression coefficients to sea state (EXP1). Another is to derive coefficients of W models in EXP1 as a function of additional wind/wave factors such as swell index, drag coefficient, and mean squared slope, deriving more nonlinear W models (EXP2). EXP2 provides reduction in Root Mean Squared Error (RMSE) by 0.1-0.3%. Sea surface drag has a stronger relationship with regression coefficients compared to swell index.These additional factors provide improved parameterizations in different wind and wave age regimes, with smaller unexplained/residual variations in W that has been a major concern in the W community.

Raman, Aishwarya↗

Nonlinear coupled rotor-fuselage helicopter vibration studies with higher harmonic control

This paper addresses the problem of vibration prediction and vibration reduction in helicopters by means of active control methodologies. The nonlinear equations of a coupled rotor/flexible-fuselage system have been derived using computer algebra, thus relegating this tedious task to the computer. In the solution procedure the trim state and vibratory response of the helicopter are obtained in a single pass by using a harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter in all the rotor and fuselage degrees of freedom. Using this solution procedure, the influence of the fuselage flexibility on the vibratory response is studied. In addition, it is shown that the conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. A new scheme called MHHC, having multiple higher harmonic pitch inputs, was used to accomplish this task of simultaneously reducing both the vibratory hub loads and fuselage vibratory response. In addition, the uniqueness of this MHHC scheme is explained in detail.

Friedmann, P. P.↗

The inward bulge type buckling of monocoque cylinders I : calculation of the effect upon the buckling stress of a compressive force, a nonlinear direct stress distribution, and a shear force

In the present part I of a series of reports on the inward bulge type buckling of monocoque cylinders the buckling load in combined bending and compression is first derived. Next the reduction in the buckling load because of a nonlinear direct stress distribution is determined. In experiments nonlinearity may result from an inadequate stiffness of the end attachments in actual airplanes from the existence of concentrated loads or cut-outs. The effect of a shearing force upon the critical load is investigated through an analysis of the results of tests carried out at GALCIT with 55 reinforced monocoque cylinders. Finally, a simple criterion of general instability is presented in the form of a buckling inequality which should be helpful to the designer of a monocoque in determining the sizes of the rings required for excluding the possibility of inward bulge type buckling.

Hoff, N J↗

Nonlinear transient analysis of joint dominated structures

A residual force technique is presented that can perform the transient analyses of large, flexible, and joint dominated structures. The technique permits substantial size reduction in the number of degrees of freedom describing the nonlinear structural models and can account for such nonlinear joint phenomena as free-play and hysteresis. In general, joints can have arbitrary force-state map representations but these are used in the form of residual force maps. One essential feature of the technique is to replace the arbitrary force-state maps describing the nonlinear joints with residual force maps describing the truss links. The main advantage of this replacement is that the incrementally small relative displacements and velocities across a joint are not monitored directly thereby avoiding numerical difficulties. Instead, very small and 'soft' residual forces are defined giving a numerically attractive form for the equations of motion and thereby permitting numerically stable integration algorithms. The technique was successfully applied to the transient analyses of a large 58 bay, 60 meter truss having nonlinear joints. A method to perform link testing is also presented.

Chapman, J. M.↗

A program for the solution of integral equations

The program, first written in REDUCE, was implemented in MACSYMA with several additional techniques which are explained. By utilizing many methods, the program can obtain closed-form and series solutions to a large class of linear and nonlinear problems. One of the techniques developed, reduction to a differential equation, has not previously appeared in the literature in the general form described.

Bogen, R. A.↗

A nonlinear structural concept for compliant walls

Two mechanisms of drag reduction for flow over flat plates were investigated. The first mechanism employs Bushnell's hypothesis that compliant walls produce drag reduction by interfering with the formation of the turbulent spots in a turbulent boundary layer. It is shown that the amplitudes and frequencies of compliant wall motions for drag reduction might be achieved by using slightly curved walls and the resulting large amplitude motions of snap buckling. A simple structural model of an arch is used in the analysis, and an asymptotic method is developed. The required wall motions can be obtained by using materials like mylar. In addition, the delay of transition from laminar to turbulent flow by driven walls was studied for Poiseuille channel flow. The walls are driven by a periodic traveling wave. A significant increase in the transitional Reynolds number is obtained by appropriately prescibing the wavelength and phase velocity of the wall motion. Previously developed asymptotic methods are used in the analysis.

Reiss, E. L.↗

Linear optimum trim solution for aircraft with three longitudinal control effectors

A simple and fast linear optimum method for trimming aircraft with a combination of three longitudinal aerodynamic or propulsive control effectors is developed, with application to preliminary design or in-flight scheduling. A Lagrangian formulation is used to determine the longitudinal load distribution which minimizes trim drag. Trim drag results obtained with the linear optimum method are similar to those obtained with a nonlinear optimum method, and significant trim drag reductions are found using either optimum method, in comparison with results obtained using various ad hoc methods.

Goodrich, Kenneth H.↗

Micromechanics Fatigue Damage Analysis Modeling for Fabric Reinforced Ceramic Matrix Composites

A micromechanics analysis modeling method was developed to analyze the damage progression and fatigue failure of fabric reinforced composite structures, especially for the brittle ceramic matrix material composites. A repeating unit cell concept of fabric reinforced composites was used to represent the global composite structure. The thermal and mechanical properties of the repeating unit cell were considered as the same as those of the global composite structure. The three-phase micromechanics, the shear-lag, and the continuum fracture mechanics models were integrated with a statistical model in the repeating unit cell to predict the progressive damages and fatigue life of the composite structures. The global structure failure was defined as the loss of loading capability of the repeating unit cell, which depends on the stiffness reduction due to material slice failures and nonlinear material properties in the repeating unit cell. The present methodology is demonstrated with the analysis results evaluated through the experimental test performed with carbon fiber reinforced silicon carbide matrix plain weave composite specimens.

Min, J. B.↗

Preliminary Nonlinear Structural Analysis of Advanced Composite Tow-Steered Shells with Large Geometric Imperfections

The structural performance of two advanced composite tow-steered shells with and without tow overlaps, and with large geometric imperfections, are predicted using linear and geometrically nonlinear finite element analyses. These shells, 35 in. long and approximately 16.3 in. diameter, are fabricated using automated fiber placement from IM7/8552 graphite/epoxy prepreg. The 8-ply,[±45/±Θ]s. shell layup incorporates a steered fiber angle Θ that varies from 10 deg. to 45 deg. periodically over the shell circumference. Shell analysis models are evaluated using geometric imperfections normalized to ±1 shell wall thickness (±0.040 in.), which are then superposed and rotated incrementally around the shell longitudinal axis. Using these nominal imperfections, the shell prebuckling axial stiffnesses and buckling loads predicted with linear and nonlinear analyses are close to reference values from linear analyses with no imperfections. The linear and nonlinear analyses are then repeated for scaled imperfections that are larger by up to a factor of 10. For these larger imperfections, linear analyses predict reductions in axial stiffnesses and buckling loads of up to 5 and 30 percent, respectively, from reference values. The nonlinear analyses predict even larger reductions in axial stiffnesses and buckling loads of up to 10 and 55 percent, respectively.

Dobrin, Calvin P.↗

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Tiffany, S. H.↗