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At least 613 records · Page 34

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NASA NTRS1985

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

Hodges, D. H.↗

NASA NTRS1985

Long-time asymptotics of a system for plasma diffusion

A system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field is discussed. It is demonstrated that the solution to this system tends to a time asymptotic state which is of space-time separable form, theta(t)f(x). Furthermore, f(x) is independent of the initial conditions and theta(t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects on radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.

Rosenau, P.↗

NASA NTRS1985

Some recent advances in computational aerodynamics for helicopter applications

The growing application of computational aerodynamics to nonlinear helicopter problems is outlined, with particular emphasis on several recent quasi-two-dimensional examples that used the thin-layer Navier-Stokes equations and an eddy-viscosity model to approximate turbulence. Rotor blade section characteristics can now be calculated accurately over a wide range of transonic flow conditions. However, a finite-difference simulation of the complete flow field about a helicopter in forward flight is not currently feasible, despite the impressive progress that is being made in both two and three dimensions. The principal limitations are today's computer speeds and memories, algorithm and solution methods, grid generation, vortex modeling, structural and aerodynamic coupling, and a shortage of engineers who are skilled in both computational fluid dynamics and helicopter aerodynamics and dynamics.

Mccroskey, W. J.↗

NASA NTRS1986

Theoretical studies of Resonance Enhanced Stimulated Raman Scattering (RESRS) of frequency doubled Alexandrite laser wavelengths in cesium vapor

This work focused on understanding the effects of arbitrary transverse and longitudinal relaxation rates on the susceptibilities of coherently driven three-level systems. The approximation of a single relaxation rate often made in previous work is strongly invalidated by the variation in the spontaneous emission lifetime between various atomic level pairs in systems such as cesium. It is of great importance to the problem of nonlinear infrared generation to determine the dependence of both real and imaginary susceptibility on relaxation rates. The imaginary susceptibility on the pump transition determines the absorption of pump photons and the imaginary susceptibility on the laser transition determines the spectral dependence of the gain. This is of particular importance for pure Raman emission (i.e., absorption at linecenter of the gain transition) as it determines the tunability characteristics we are aiming to predict. The real susceptibility is important when cavities are used at the signal field as this will determine the loaded resonance of the Raman oscillator. Researchers show that in some cases which result from having different relaxation rates mode splitting may result, allowing more than one frequency to have the same Raman wavelength, possibly resulting in a temporal instability.

Lawandy, N. M.↗

NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗

NASA NTRS1987

Evaluation of on-line pulse control for vibration suppression in flexible spacecraft

On-line pulse control for vibration suppression in a flexible spacecraft was evaluated. A continuous beam vs. a truss was modeled. A linear finite element model was used to determine the truss characteristics. Control issues outlined are ED pulse actuator development, pseudo pulse algorithm development, and large nonlinear simulation problems.

Bekey, G. A.↗

NASA NTRS1987

Computable optimal value bounds for generalized convex programs

It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated.

Fiacco, Anthony V.↗

NASA NTRS1987

Stability of streamwise vortices

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Khorrami, M. K.↗

NASA NTRS1987

Optimal placement of critical speeds in rotor-bearing systems

The design of a rotor-bearing system is an iterative process in which the parameters that influence the design are modified until the desired design objectives are achieved. Primary among the design objectives is the minimization of the response amplitude within the operating range of the rotor system. An automated design procedure for the optimal placement of the critical speeds of a rotor is presented. The desired design objective is cast as a nonlinear programming problem that minimizes an objective function subject to constraints. The optimization program interacts with an analysis program to search for the feasible optimal design.

Rajan, M.↗

NASA NTRS1987

Vortex breakdown simulation based on a nonlinear inviscid model

It is shown that the inviscid equations governing steady axisymmetric flow with swirl, admit solutions with closed streamlines. Results are obtained using two different numerical algorithms. The first is based on a multigrid method for nonlinear eigenvalue problems, while the second is based on a least squares formulation.

Hafez, M. M.↗

NASA NTRS1987

SHARP simulation of discontinuities in highly convective steady flow

For steady multidimesional convection, the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme has several attractive properties. However, for highly convective simulation of step profiles, QUICK produces unphysical overshoots and a few oscillations, and this may cause serious problems in nonlinear flows. Fortunately, it is possible to modify the convective flux by writing the normalized convected control-volume face value as a function of the normalized adjacent upstream node value, developing criteria for monotonic resolution without sacrificing formal accuracy. This results in a nonlinear functional relationship between the normalized variables, whereas standard methods are all linear in this sense. The resulting Simple High Accuracy Resolution Program (SHARP) can be applied to steady multidimensional flows containing thin shear or mixing layers, shock waves, and other frontal phenomena. This represents a significant advance in modeling highly convective flows of engineering and geophysical importance. SHARP is based on an explicit, conservative, control-volume flux formation, equally applicable to one, two, or three dimensional elliptic, parabolic, hyperbolic, or mixed-flow regimes. Results are given for the bench-mark purely convective first-order results and the nonmonotonic predictions of second- and third-order upwinding.

Leonard, B. P.↗

NASA NTRS1988

Some rotorcraft applications of computational fluid dynamics

The growing application of computational aerodynamics to nonlinear rotorcraft problems is outlined, with particular emphasis on the development of new methods based on the Euler and thin-layer Navier-Stokes equations. Rotor airfoil characteristics can now be calculated accurately over a wide range of transonic flow conditions. However, unsteady 3-D viscous codes remain in the research stage, and a numerical simulation of the complete flow field about a helicopter in forward flight is not now feasible. Nevertheless, impressive progress is being made in preparation for future supercomputers that will enable meaningful calculations to be made for arbitrary rotorcraft configurations.

Mccroskey, W. J.↗

NASA NTRS1988

Some rotorcraft applications of computational fluid dynamics

Mccroskey, W. J.↗

NASA NTRS1988

Application of fuzzy theories to formulation of multi-objective design problems

Much of the decision making in real world takes place in an environment in which the goals, the constraints, and the consequences of possible actions are not known precisely. In order to deal with imprecision quantitatively, the tools of fuzzy set theory can by used. This paper demonstrates the effectiveness of fuzzy theories in the formulation and solution of two types of helicopter design problems involving multiple objectives. The first problem deals with the determination of optimal flight parameters to accomplish a specified mission in the presence of three competing objectives. The second problem addresses the optimal design of the main rotor of a helicopter involving eight objective functions. A method of solving these multi-objective problems using nonlinear programming techniques is presented. Results obtained using fuzzy formulation are compared with those obtained using crisp optimization techniques. The outlined procedures are expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.

Dhingra, A. K.↗

NASA NTRS1989

Algorithm Estimates Microwave Water-Vapor Delay

Accuracy equals or exceeds conventional linear algorithms. "Profile" algorithm improved algorithm using water-vapor-radiometer data to produce estimates of microwave delays caused by water vapor in troposphere. Does not require site-specific and weather-dependent empirical parameters other than standard meteorological data, latitude, and altitude for use in conjunction with published standard atmospheric data. Basic premise of profile algorithm, wet-path delay approximated closely by solution to simplified version of nonlinear delay problem and generated numerically from each radiometer observation and simultaneous meteorological data.

Robinson, Steven E.↗

NASA NTRS1989

Microcomputer based controller for the Langley 0.3-meter Transonic Cryogenic Tunnel

Flow control of the Langley 0.3-meter Transonic Cryogenic Tunnel (TCT) is a multivariable nonlinear control problem. Globally stable control laws were generated to hold tunnel conditions in the presence of geometrical disturbances in the test section and precisely control the tunnel states for small and large set point changes. The control laws are mechanized as four inner control loops for tunnel pressure, temperature, fan speed, and liquid nitrogen supply pressure, and two outer loops for Mach number and Reynolds number. These integrated control laws have been mechanized on a 16-bit microcomputer working on DOS. This document details the model of the 0.3-m TCT, control laws, microcomputer realization, and its performance. The tunnel closed loop responses to small and large set point changes were presented. The controller incorporates safe thermal management of the tunnel cooldown based on thermal restrictions. The controller was shown to provide control of temperature to + or - 0.2K, pressure to + or - 0.07 psia, and Mach number to + or - 0.002 of a given set point during aerodynamic data acquisition in the presence of intrusive geometrical changes like flexwall movement, angle-of-attack changes, and drag rake traverse. The controller also provides a new feature of Reynolds number control. The controller provides a safe, reliable, and economical control of the 0.3-m TCT.

Balakrishna, S.↗

NASA NTRS1989

Numerical simulation of Goertler/Tollmien-Schlichting wave-interaction

The problem of nonlinear development of Goertler vortices and interaction with Tollmien-Schlichting (TS) waves is considered within the framework of incompressible Navier-Stokes equations which are solved by a Fourier-Chebyshev spectral method. It is shown that two-dimensional waves can be excited in the flow modulated by Goertler vortices. Due to nonlinear effects, this interaction further leads to the development of oblique waves with spanwise wavelength equal to the Goertler vortex wavelength. Interaction is also considered of oblique waves with spanwise wavelength twice that of Goertler vortices.

Malik, M. R.↗

NASA NTRS1989

Computational Methods for Structural Mechanics and Dynamics, part 1

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Stroud, W. Jefferson↗