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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Bielawa, R. L.↗
NASA NTRS1964

Analytical Solutions for Non-Linear Differential Equations with the Help of a Digital Computer

A technique was developed with the help of a digital computer for analytic (algebraic) solutions of autonomous and nonautonomous equations. Two operational transform techniques have been programmed for the solution of these equations. Only relatively simple nonlinear differential equations have been considered. In the cases considered it has been possible to assimilate the secular terms into the solutions. For cases where f(t) is not a bounded function, a direct series solution is developed which can be shown to be an analytic function. All solutions have been checked against results obtained by numerical integration for given initial conditions and constants. It is evident that certain nonlinear differential equations can be solved with the help of a digital computer.

Cromwell, P. C.↗
NASA NTRS1977

Displacement incrementation in non-linear structural analysis by the self-correcting method

The prediction of nonlinear structural behavior by the finite element method wherein buckling does not occur has received considerable attention and, with it, reasonable success has been achieved. However, the post-buckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered. This note reviews very briefly the numerical methods currently being used for pre- and post-buckling analysis and presents a self-correcting approach based on load and displacement incrementation which is shown to be efficient, reliable, and easy to program. Numerical solutions are presented which demonstrate the effectiveness of the method.

Haisler, W. E.↗
NASA NTRS1977

Non-linear propagation of complex sound fields in rectangular ducts. I - The self-excitation phenomenon

Nonlinear acoustic interactions at the second order (so-called weak interactions) of the perturbation scheme have been recognized for a long time. This paper examines the possibility of stronger interactions at the first order which are found in rigid rectangular ducts and to a lesser degree in slightly soft rectangular ducts. The strong interactions occur if any two modes have identical phase speeds, the case of multimode and multifrequency input for example. An important consequence of the strong interaction is the self-generation of subharmonics. Even a small amount of subharmonic can, given the right phase conditions, grow through a strong interaction with a higher harmonic.

Vaidya, P. G.↗
NASA NTRS1977

Non-linear analysis of vibrations of irregular plates

A numerical perturbation method is used to investigate the forced vibrations of irregular plates. Nonlinear terms associated with the midplane stretching are retained in the analysis. The numerical part of the method involves the use of linear, finite element techniques to determine the free oscillation mode shapes and frequencies and to obtain the linear midplane stress resultants caused by the midplane stretching. Representing the solution as an expansion in terms of these linear mode shapes, these modes and the resultants are used to determine the equations governing the time-dependent coefficients of this expansion. These equations are solved by using the method of multiple scales. Specific solutions are given for the main-resonant vibrations of an elliptical plate in the presence of internal resonances. The results indicate that modes other than the driven mode can be drawn into the steady state response. Though the excitation is composed of a single harmonic, the response may not be periodic. Moreover, the particular types of responses that can occur are highly dependent on the mode being excited and are sensitive to small geometrical changes.

Lobitz, D. W.↗
NASA NTRS1978

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Khosla, P. K.↗
NASA NTRS1977

Non-linear duct acoustics and its application to fan noise

Quite often the scalar Helmholtz equation is assumed to be the fundamental equation of duct acoustics and various relations are derived from it. An investigation is, therefore, conducted regarding the underlying assumptions leading to the Helmholtz equation. It is found that serious errors, even well below 186 dB, are possible if the assumption of linearity were to be made. In duct acoustics these errors are highest near the cutoff points and in the case of ducts with transonic flow. It is pointed out that serious errors could arise if a nonlinear problem is analyzed by linear methods. At times, an entire phenomenon remains unpredictable by linear methods. Attention is given to the characteristics of nonlinear systems, the phenomenon of multiple pure tones in the case of noise from the aircraft engine fans, the limitations of the conventional acoustics equation, duct shape and nonlinearity, and the numerical simulation of a fan with 8 blades.

Vaidya, P. G.↗
NASA NTRS1978

Study of the effect of static/dynamic Coulomb friction variation at the tape-head interface of a spacecraft tape recorder by non-linear time response simulation

A description is presented of six simulation cases investigating the effect of the variation of static-dynamic Coulomb friction on servo system stability/performance. The upper and lower levels of dynamic Coulomb friction which allowed operation within requirements were determined roughly to be three times and 50% respectively of nominal values considered in a table. A useful application for the nonlinear time response simulation is the sensitivity analysis of final hardware design with respect to such system parameters as cannot be varied realistically or easily in the actual hardware. Parameters of the static/dynamic Coulomb friction fall in this category.

Mukhopadhyay, A. K.↗
NASA NTRS1979

Non-linear phenomena in films of solar arrays

The paper assesses nonlinear effects in films which are associated with the instability of their shape as a result of contractions during longitudinal and transverse in-plane oscillations. The following problems are solved analytically: transverse in-plane oscillations, longitudinal oscillations in films of rotating solar sail, transverse in-plane oscillations in films of a rotating solar sail, and effect of damping in films of a rotating solar sail. The reason for damping lies in the loss of kinetic energy during absorption of the film particles by root wrinkles without reflection (absolutely inelastic shock).

Zak, M.↗
NASA NTRS1979

Non-linear dynamic response of a wind turbine blade

The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.

Chopra, I.↗
NASA NTRS1980

Output feedback non-linear decoupled control synthesis and observer design for manoeuvring aircraft

A study of the applicability of nonlinear decoupling theory to the design of control systems using output feedback for maneuvering aircraft is presented. The response variables chosen for decoupled control were angular velocity components along roll, pitch, and yaw axes, angle of attack (p), and angle of sideslip, using aileron, rudder, and elevator controls. An observer design for a class of nonlinear systems was presented and this method was used to estimate angle of attack and sideslip; an approximate observer was obtained by neglecting derivatives of p and aileron deflection angles and it was used in a simulation study. A simulation study showed that precise rapid combined lateral and longitudinal maneuvers can be performed; it was also demonstrated that a bank-angle-command outer loop could be designed for precise bank angles changes and simultaneous large lift maneuvers.

Singh, S. N.↗
NASA NTRS1979

Surprisal analysis of rotational-translational energy transfer - Non-linear versus linear rotors

Surprisal versus energy gap analyses of state-to-state cross sections are presented for a number of linear rigid rotors excited by collisions with atoms for H2-H, H2-He, HCl-He, HCl-Ar, CO-He, CS-H2 (j=0) OCS-H2 (j=0) and HN2(+)-He, where (j=0) indicates that the hydrogen molecule was constrained to remain in its lowest level. Different systems exhibit wide variations in the slope of the surprisal plot and in certain cases, enough to indicate that the energy gap may not be the static dynamical constraint. Similar analyses are presented for nonlinear rotors excited by atoms for H2CO-He and H2O-He. For these, the data show a great deal of scatter, indicating that the reduced energy gap is probably not the appropriate independent variable.

Green, S.↗
NASA NTRS1981

Non-linear stability around the triangular libration points

The configuration space around the triangular libration points in the Earth-Moon system is partitioned according to the stability of the motion. The regions around L4 and L5 are established where particles placed with zero initial velocity will librate. The complexity of the partitioning is revealed.

Mckenzie, R.↗
NASA NTRS1981

A nonparametric identification method for a class of non-linear systems

A relatively simple nonparametric method for the identification of a class of close-coupled nonlinear multi-degree-of-freedom systems has been developed. The identification of arbitrary memoryless nonlinearities is possible through knowledge of the accelerations, velocities, and displacements of the various masses. These quantities are used to obtain the surfaces of the restoring forces as functions of the intermass displacements and velocities. The method was demonstrated by application to a four-degree-of-freedom system to identify the restoring forces. It is found that the identification results are relatively insensitive to measurement noise.

Udwadia, F. E.↗
NASA NTRS1981

Non-linear propagation in near sonic flows

A nonlinear analysis is developed for sound propagation in a variable-area duct in which the mean flow approaches choking conditions. A quasi-one-dimensional model is used and the nonlinear analysis represents the acoustic disturbance as a sum of interacting harmonics. The numerical procedure is stable for cases of strong interaction and is able to integrate through the throat region without any numerical instability.

Nayfeh, A. H.↗
NASA NTRS1981

Research and development program for non-linear structural modeling with advanced time-temperature dependent constitutive relationships

Results of a 20-month research and development program for nonlinear structural modeling with advanced time-temperature constitutive relationships are reported. The program included: (1) the evaluation of a number of viscoplastic constitutive models in the published literature; (2) incorporation of three of the most appropriate constitutive models into the MARC nonlinear finite element program; (3) calibration of the three constitutive models against experimental data using Hastelloy-X material; and (4) application of the most appropriate constitutive model to a three dimensional finite element analysis of a cylindrical combustor liner louver test specimen to establish the capability of the viscoplastic model to predict component structural response.

Walker, K. P.↗