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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Nonlinear ordinary difference equations

Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

Caughey, T. K.↗
NASA NTRS1979

Nonlinear structural crash dynamics analyses

Presented in this paper are the results of three nonlinear computer programs, KRASH, ACTION and DYCAST used to analyze the dynamic response of a twin-engine, low-wing airplane section subjected to a 8.38 m/s (27.5 ft/s) vertical impact velocity crash condition. This impact condition simulates the vertical sink rate in a shallow aircraft landing or takeoff accident. The three distinct analysis techniques for nonlinear dynamic response of aircraft structures are briefly examined and compared versus each other and the experimental data. The report contains brief descriptions of the three computer programs, the respective aircraft section mathematical models, pertinent data from the experimental test performed at NASA Langley, and a comparison of the analyses versus test results. Cost and accuracy comparisons between the three analyses are made to illustrate the possible uses of the different nonlinear programs and their future potential.

Hayduk, R. J.↗
NASA NTRS1980

Wing/store flutter with nonlinear pylon stiffness

Recent wind tunnel tests and analytical studies show that a store mounted on a pylon with soft pitch stiffness provides substantial increase in flutter speed of fighter aircraft and reduces dependency of flutter on mass and inertia of the store. This concept, termed the decoupler pylon, utilizes a low frequency control system to maintain pitch alignment of the store during maneuvers and changing flight conditions. Under rapidly changing transient loads, however, the alignment control system may allow the store to momentarily bottom against a relatively stiff backup structure in which case the pylon stiffness acts as a hardening nonlinear spring. Such structural nonlinearities are known to affect not only the flutter speed but also the basic behavior of the instability. The influence of pylon stiffness nonlinearities or the flutter characteristics of wing mounted external stores is examined.

Desmarais, R. N.↗
NASA NTRS1980

Theoretical prediction of nonlinear propagation effects on noise signatures generated by subsonic or supersonic propeller or rotor-blade tips

The nonlinear propagation equations for sound generated by a constant speed blade tip are presented. Propagation from a subsonic tip is treated as well as the various cases that can occur at supersonic speeds. Some computed examples indicate that the nonlinear theory correlates with experimental results better than linear theory for large amplitude waves. For swept tips that generate a wave with large amplitude leading expansion, the nonlinear theory predicts a cancellation effect that results in a significant reduction of both amplitude and impulse.

Barger, R. L.↗
NASA NTRS1980

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Kamat, M. P.↗
NASA NTRS1980

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗
NASA NTRS1980

Nonlinear calculation of a radial mode of oscillation of a hot white dwarf

A linearly unstable first harmonic radial mode of oscillation (period 0.86 s) of a hot white dwarf with a hydrogen envelope is analyzed in the nonlinear regime by application of the Stellingwerf technique to a nonlinear hydrocode. The mass and equilibrium luminosity of the hot white dwarf are 1.3 solar masses, and 1.6 x 10 to the 37th erg/s, respectively. A stable nonlinear mode is found to exist, in which appreciable shock damping occurs at and near the surface - the shock damping being the dominant stabilizing effect. This enhances the possibility that such an object can produce a pulsating X-ray source.

Degregoria, A. J.↗
NASA NTRS1980

Wing/store flutter with nonlinear pylon stiffness

Recent wind tunnel tests and analytical studies show that a store mounted on a pylon with 'soft' pitch stiffness provides substantial increase in flutter speed of fighter aircraft and reduces dependency of flutter on mass and inertia of the store. This concept, termed the decoupler pylon, utilizes a low-frequency control system to maintain pitch alignment of the store during maneuvers and changing flight conditions. Under rapidly changing transient loads, however, the alignment control system may allow the store to momentarily bottom against a relatively stiff backup structure in which case the pylon stiffness acts as a hardening nonlinear spring. Such structural nonlinearities are known to affect not only the flutter speed but also the basic behavior of the instability. This paper examines the influence of pylon stiffness nonlinearities on the flutter characteristics of wing-mounted external stores.

Desmarais, R. N.↗
NASA NTRS1980

Energy minimization versus pseudo force technique for nonlinear structural analysis

The effectiveness of using minimization techniques for the solution of nonlinear structural analysis problems is discussed and demonstrated by comparison with the conventional pseudo force technique. The comparison involves nonlinear problems with a relatively few degrees of freedom. A survey of the state-of-the-art of algorithms for unconstrained minimization reveals that extension of the technique to large scale nonlinear systems is possible.

Kamat, M. P.↗
NASA NTRS1980

Pseudosteady state analysis of nonlinear aircraft maneuvers

An analytical method has been developed for studying the combined effects of rotational coupling and nonlinear aerodynamics on aircraft response for specified control inputs. The method involves the simultaneous solution of two nonlinear equations which are functions of angle of attack, roll rate, and the control inputs. The method is applied to a number of maneuvers for a fighter type aircraft. Time history responses verified the usefulness of the analysis for predicting a variety of response characteristics caused by interacting nonlinear aerodynamic and inertial effects, including spin conditions.

Young, J. W.↗
NASA NTRS1978

Numerical derivation of linear perturbation model from nonlinear real-time vehicle simulations - A means of validation and increased credibility

A numerical technique has been developed which generates linear perturbation models from nonlinear real-time aircraft vehicle simulations at Langley Research Center. The technique is very general and can be applied to simulations of any system described by nonlinear differential equations. Linear models about various trim conditions have been obtained from simulations of the Boeing 737, Northrop F5-E, Cessna 180, Sikorsky CH-54, and NASA/Army Rotor Systems Research Aircraft (RSRA). One use of the derived linear models is as a validation and verification tool for the nonlinear simulation.

Dieudonne, J. E.↗
NASA NTRS1980

Pseudosteady-state analysis of nonlinear aircraft maneuvers

An analytical method was developed for studying the combined effects of rotational coupling and nonlinear aerodynamics on aircraft response for specified control inputs. The method involves the simultaneous solution of two nonlinear equations which are functions of angle attack, roll rate, and control inputs. The method was applied to a number of maneuvers for a fighter-type aircraft. Time history responses verified the usefulness of the analysis for predicting a variety of response characteristics caused by interacting nonlinear aerodynamic and inertial effects, including spin conditions.

Young, J. W.↗
NASA NTRS1980

Nonlinear grid error effects on numerical solution of partial differential equations

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Dey, S. K.↗
NASA NTRS1981

A rapid perturbation procedure for determining nonlinear flow solutions: Application to transonic turbomachinery flows

Perturbation procedures and associated computational codes for determining nonlinear flow solutions were developed to establish a method for minimizing computational requirements associated with parametric studies of transonic flows in turbomachines. The procedure that was developed and evaluated was found to be capable of determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameter. Coordinate straining is employed to account for the movement of discontinuities and maxima of high gradient regions due to the perturbation. The development and results reported are for the single parameter perturbation problem. Flows past both isolated airfoils and compressor cascades involving a wide variety of flow and geometry parameter changes are reported. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure.

Stahara, S. S.↗
NASA NTRS1981

Development of a nonlinear vortex method

Progress is reported in the development of reliable nonlinear vortex methods for predicting the steady and unsteady aerodynamic loads of highly sweptback wings at large angles of attack. Abstracts of the papers, talks, and theses produced through this research are included. The modified nonlinear discrete vortex method and the nonlinear hybrid vortex method are highlighted.

Kandil, O. A.↗
NASA NTRS1981

Nonlinear viscoelastic characterization of thin polyethylene film

In order to understand the state of stress and strain in a typical balloon fabricated from thin polyethylene film, experiment data in the literature reviewed. It was determined that the film behaves as a nonlinear viscoelasticity material and should be characterized accordingly. A simple uniaxial, nonlinear viscoelastic model was developed for predicting stress given a certain strain history. The simple model showed good qualitative agreement with results of constant rate, uniaxial accurately predicting stresses for cyclic strain histories typical of balloon flights. A program was outlined which will result in the development of a more complex nonlinear viscoelastic model.

Wilbeck, J. S.↗
NASA NTRS1980

Finite-element analysis of nonlinear conduction problems subject to moving fields

Through the use of a space-time warp, specialized moving finite elements are developed that can be employed to generate a nonlinear heat conduction model for situations involving traveling boundary and heat generation fields superposed on an initial state. To facilitate the solution of the resulting nonlinear finite-element formulation, a multilevel heuristic iterative solution strategy is developed. In order to demonstrate the versatility and accuracy of the moving elements and their associated nonlinear solution strategy, the results of several numerical experiments are presented.

Padovan, J.↗
NASA NTRS1980

A modified Barrett-Lampard expansion and its application to bandpass nonlinearities with both AM-AM and AM-PM conversion

A two-dimensional Barrett-Lampard expansion is developed to handle two-dimensional nonlinear systems with random Gaussian inputs. The theory is applied to the problem of evaluating the mean signal and the inphase and quadrature noise correlation functions at the output of a TWT nonlinearity exhibiting arbitrary AM-AM and AM-PM characteristics, when the input consists of a narrow-band signal and Gaussian noise. As a specialized application, the classical problem of determining the coherent and incoherent noise correlation functions at the output of a power-law bandpass nonlinearity is also considered. The results are of interest in assessing the performance of coherent satellite communication channels. The theory developed is accompanied by numerical examples of practical interest.

Chie, C. M.↗