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At least 1,279 records · Page 71
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NASA NTRS1974

Attenuation characteristics of nonlinear pressure waves propagating in pipes

A series of experiments was conducted to investigate temporal and spatial velocity distributions of fluid flow in 3-in. open-end pipes of various lengths up to 210 ft, produced by the propagation of nonlinear pressure waves of various intensities. Velocity profiles across each of five sections along the pipes were measured as a function of time with the use of hot-film and hot-wire anemometers for two pressure waves produced by a piston. Peculiar configurations of the velocity profiles across the pipe section were noted, which are uncommon for steady pipe flow. Theoretical consideration was given to this phenomenon of higher velocity near the pipe wall for qualitative confirmation. Experimentally time-dependent velocity distributions along the pipe axis were compared with one-dimensional theoretical results obtained by the method of characteristics with or without diffusion term for the purpose of determining the attenuation characteristics of the nonlinear wave propagation in the pipes.

Shih, C. C.↗
NASA NTRS1974

Connective stability of nonlinear matrix systems

Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.

Siljak, D. D.↗
NASA NTRS1974

Estimation of nonlinear aerodynamic derivatives of a variable geometry fighter aircraft from flight data

This paper is concerned with the estimation of stability and control parameters of a high performance fighter aircraft from data obtained from high angle of attack flight. The estimation process utilizes a maximum likelihood algorithm derived for the case of a nonlinear aerodynamic force and moment model. The aircraft used was a high speed variable sweep heavy weight fighter with twin vertical tails. Comparisons of results from the nonlinear analysis are made with linear theory and wind tunnel results when available.

Ramachandran, S.↗
NASA NTRS1974

Theoretical investigation of nonlinear three-dimensional instabilities in liquid rockets with real nozzles

An approximate analytical technique has been developed for the solution of nonlinear three-dimensional, transverse and axial combustion-instability problems that are frequently observed in liquid-propellant rocket motors. This theory is an extension and generalization of previous analyses, which could analyze either transverse or axial instabilities in liquid combustors with quasi-steady nozzles, to the practical situations of three-dimensional instabilities in combustors with conventional DeLaval nozzles. Unlike the quasi-steady nozzle, the presence of a conventional nozzle imposes restrictions upon the behavior of both the amplitudes and phases of the oscillations at the nozzle entrance plane. The applicability of the solution technique, which is based on the Galerkin method, is demonstrated by analyzing the nonlinear stability of a cylindrical liquid-rocket combustor with uniform injection of propellants at one end and a conventional nozzle at the other end. Crocco's pressure-sensitive time-lag model is used to describe the unsteady combustion process.

Powell, E. A.↗
NASA NTRS1975

Numerical nonlinear inelastic analysis of stiffened shells of revolution. Volume 1: Theory manual for STARS-2P digital computer program

The theoretical analysis background for the STARS-2P nonlinear inelastic program is discussed. The theory involved is amenable for the analysis of large deflection inelastic behavior in axisymmetric shells of revolution subjected to axisymmetric loadings. The analysis is capable of considering such effects as those involved in nonproportional and cyclic loading conditions. The following are also discussed: orthotropic nonlinear kinematic hardening theory; shell wall cross sections and discrete ring stiffeners; the coupled axisymmetric large deflection elasto-plastic torsion problem; and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions.

Svalbonas, V.↗
NASA NTRS1975

A triangular thin shell finite element: Nonlinear analysis

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Thomas, G. R.↗
NASA NTRS1975

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗
NASA NTRS1974

Nonlinear theory of electron neutralization waves in ions beams with dissipation

An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.

Wilhelm, H. E.↗
NASA NTRS1975

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

Smith, L. L.↗
NASA NTRS1975

Empirical comparison of a linear and a nonlinear washout for motion simulators

The subjective opinions gathered from seven pilots in the process of comparing a linear and a nonlinear washout for motion simulators reveal an important advance in motion cue presentation. The advance is not in the increased cue provided by the nonlinear filter over a linear filter for the same amount of motion base travel, but rather in the elimination of false rotational rate cues presented by linear filters.

Parrish, R. V.↗
NASA NTRS1974

Nonlinear finite-element analysis of laminated composite shells

Two aspects of the geometrically nonlinear analysis of laminated composite shells are considered in this paper. The first pertains to the simplifications and computational advantages resulting from the use of group-theoretic methods in conjunction with computerized symbolic (algebraic) manipulation in the element development. The second aspect pertains to the combined effects of shear deformation and nonlinearity on the accuracy and convergence of two-dimensional, shear-flexible stiffness finite element models.

Noor, A. K.↗
NASA NTRS1975

Nonlinear transient neutralization theory of ion beams with dissipation

An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions. The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave. This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasi-neutral beam results. The relaxation scale in space agrees with neutralization experiments of rarefied ion beams, if the collective momentum transfer between the electron and ion streams is assumed to be of the Buneman type.

Wilhelm, H. E.↗
NASA NTRS1975

Nonlinear hyperbolic theory of thermal waves in metals

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

Wilhelm, H. E.↗
NASA NTRS1975

Nonlinear vibration of cylindrical shells

The large amplitude vibration of a thin-walled cylindrical shell is analyzed. A perturbation method is used to solve the steady-state forced vibration problem. The simply-supported boundary conditions and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental mode, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental mode. Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinearity is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. An experimental investigation is conducted, and the results are in qualitative agreement with the theory. 'Nonstationary' response is detected at some frequencies for large amplitude response in which the amplitude drifts from one value to another. Various nonlinear phenomena are observed and comparisons with the theoretical results are made.

Chen, J. C.↗
NASA NTRS1975

Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field

Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.

Hague, D. S.↗
NASA NTRS1975

An in-flight simulation of lateral control nonlinearities

An in-flight simulation program was conducted to explore, in a generalized way, the influence of spoiler-type roll-control nonlinearities on handling qualities. The roll responses studied typically featured a dead zone or very small effectiveness for small control inputs, a very high effectiveness for mid-range deflections, and low effectiveness again for large inputs. A linear force gradient with no detectable breakout force was provided. Given otherwise good handling characteristics, it was found that moderate nonlinearities of the types tested might yield acceptable roll control, but the best level of handling qualities is obtained with linear, aileron-like control.

Ellis, D. R.↗
NASA NTRS1975

PLANS: A finite element program for nonlinear analysis of structures. Volume 1: Theoretical manual

The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.

Pifko, A.↗
NASA NTRS1976

A technique using a nonlinear helicopter model for determining trims and derivatives

A technique is described for determining the trims and quasi-static derivatives of a flight vehicle for use in a linear perturbation model; both the coupled and uncoupled forms of the linear perturbation model are included. Since this technique requires a nonlinear vehicle model, detailed equations with constants and nonlinear functions for the CH-47B tandem rotor helicopter are presented. Tables of trims and derivatives are included for airspeeds between -40 and 160 knots and rates of descent between + or - 10.16 m/sec (+ or - 200 ft/min). As a verification, the calculated and referenced values of comparable trims, derivatives, and linear model poles are shown to have acceptable agreement.

Ostroff, A. J.↗