SEARCH · Search NASA

Results for “nonlinear”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33

All sources NASA NTRS DOE OSTI

NASA NTRS1986

A nonlinear substructuring method for concurrent processing computers

This paper proposes a method, based on substructuring, to solve nonlinear structural analysis problems on multiprocessor computers. Background information is given on the use of substructuring in large-scale finite element programs and computational time distributions for the major components for an example nonlinear finite element analysis are discussed. Implementation of the substructuring method on a typical multiprocessor computer is described and estimates are made of expected reductions in computation times based on nonlinear substructuring results obtained on a single processor computer.

Storaasli, O. O.↗

NASA NTRS1986

Identification of nonlinear system parameters in joints using the force-state mapping technique

A procedure is presented for identifying the potentially strong nonlinear properties of structural members, such as joints, by expressing the force transmitted by the member as a function of its mechanical state. By explicitly including position and rate dependent effects, the surface of transmitted force versus state, the force-state map, has distinct, unique, superposable features for common structural nonlinearities, even those which appear to indicate hysteresis on a force-stroke presentation. An analysis is performed on the influence of true memory effects, transient response, and uncertainty in the measurements and system mass on the precision of the procedure. The successful identification of simulated data verifies the accuracy of the identification algorithm. Tests are then conducted on three actual joint models, with incomplete state measurements typical of an actual testing environment. The ability of the procedure to estimate the complete state vector and to analyze and reconstruct the measured nonlinear characteristics is demonstrated.

Crawley, E. F.↗

NASA NTRS1986

Effects of nonlinear damping on random response of beams to acoustic loading

Effects of both nonlinear damping and large-deflection are included in the theoretical analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peak and the increase of the modal frequency. Two nonlinear damping models are considered in the analysis using a single-mode approach. Mean square maximum deflection, mean square maximum strain, and spectral density function of maximum strain for simply supported and clamped beams are obtained. It is demonstrated that nonlinear damping contributes significantly to the broadening of the response peak and to the mean square maximum deflection and strain.

Mei, C.↗

NASA NTRS1986

A canonical expansion for nonlinear systems

The importance of differential geometry, particularly Lie brackets of vector fields, in the study of nonlinear systems is well established. Under very mild assumptions, it is shown that a real-analytic nonlinear system has an expansion in which the coefficients are computed in terms of Lie brackets. This expansion occurs in a special coordinate system. The concept of a pure feedback system is also explained. For control design involving a nonlinear system, one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths.

Su, R.↗

NASA NTRS1986

Response of symmetric rectangular composite laminates with nonlinear damping subjected to acoustic loading

Effects of both nonlinear damping and large-deflection are included in the analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening and flattening out of the strain response peaks and the increasing of the response frequency. A nonlinear damping model is considered in the analysis using a single-mode approach. Root-mean-square (RMS) maximum deflection, RMS strains, spectral density functions of strain, and equivalent linear frequency are obtained for clamped and simply supported rectangular symmetric laminated composite plates. It is demonstrated that nonlinear damping is the one which causes the broadening of the response peaks, and it has great influence on RMS panel deflection, RMS strains, and frequency.

Mei, C.↗

NASA NTRS1986

On the Nonlinearity of Modern Shock-Capturing Schemes

The development is reviewed of shock capturing methods, paying special attention to the increasing nonlinearity in the design of numerical schemes. The nature is studies of this nonlinearity and its relation to upwind differencing is examined. This nonlinearity of the modern shock capturing methods is essential, in the sense that linear analysis is not justified and may lead to wrong conclusions. Examples to demonstrate this point are given.

Harten, A.↗

NASA NTRS1987

Dynamics of trusses having nonlinear joints

The transient analysis of trusses having nonlinear joints can be accomplished using the residual force technique. The technique was applied a two degree of freedom spring mass system, a four bay planar truss, and an actual ten bay deployable truss. Joints chosen for analysis were the nonlinear gap joints and the linear Voigt joints. Results from the nonlinear gap analyses generally indicate that coupling between the modes can display some interesting effects during free vibration. One particularly interesting effect was that the damping of the structure appeared to be higher than could be accounted for from modal damping alone. Energy transferral from the lower to the higher modes was found to exist as a result of the modal coupling. The apparently increased damping was due to the fact that the energy transferred to the higher modes is inherently dissipated more quickly. Another interesting phenomenon was that the lower modes could drive the higher modes even during free vibration and that these modes could display a rather large quasi-steady state behavior even when modal damping was present. Gaps were also found to increase the amplitude and period of the free vibration response as expected.

Chapman, J. M.↗

NASA NTRS1987

Hamiltonian theory of nonlinear waves in planetary rings

The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.

Stewart, G. R.↗

NASA NTRS1986

The evolution of nonlinear Alfven waves subject to growth and damping

The effects of wave amplification (by streaming particle distributions) and damping (by ion-cyclotron resonance absorption) on the nonlinear evolution of Alfven waves are investigated theoretically. The results of numerical simulations based on the derivative-Schroedinger-equation model of Spangler and Sheerin (1983 and 1985) are presented graphically and characterized in detail, with an emphasis on astrophysical applications. Three phases of wave-packet evolution (linear, nonlinear-saturation, and postsaturation quasi-steady) are identified, and nonlinearity is found to transfer wave energy from growing or amplified wavenumbers to wavenumbers affected by damping. It is pointed out that although there are similarities between the solitonlike pulses predicted by the simulations and short-wavelength shocklet structures observed in the earth bow shock, the model does not explain why low-frequency waves stop growing in the vicinity of the bow shock.

Spangler, S. R.↗

NASA NTRS1986

Multiply scaled constrained nonlinear equation solvers

To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

Padovan, Joe↗

NASA NTRS1987

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial stength in graphite/epoxy composites.

Prosser, William H.↗

NASA NTRS1988

A nonlinear filtering process diagnostic system for the Space Station

A nonlinear filtering process diagnostic system, terrestrial simulation and real time implementation studies is presented. Possible applications to Space Station subsystem elements are discussed. A process diagnostic system using model based nonlinear filtering for systems with random structure was shown to provide improvements in stability, robustness, and overall performance in comparison to linear filter based systems. A suboptimal version of the nonlinear filter (zero order approximation filter, or ZOA filter) was used in simulation studies, initially, with a pressurized water reactor model and then with water/steam heat exchanger models. Finally, a real time implementation for leak detection in a water/steam heat exchanger was conducted using the ZOA filter and heat exchanger models.

Yoel, Raymond R.↗

NASA NTRS1988

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Rosen, I. G.↗

NASA NTRS1987

Integrating nonlinear aerodynamic and structural analysis for a complete fighter configuration

The coupling of a nonlinear aerodynamics program with a structural analysis program to include the effects of static aeroelasticity in early preliminary design studies is described. A nonlinear, full potential aerodynamics method with capability to model geometric details of a complete aircraft in supersonic flow is used. The deflections of the lifting surfaces are calculated using an equivalent plate structural representation which can readily accommodate the changes in stiffness and geometric properties required during the preliminary design process. An iterative solution procedure is used to obtain consistent aerodynamic loads and structural deflections at the specified flight conditions. The volume of data transmitted between programs is minimized. The procedure is applied to a complete aircraft and the numerical results illustrate the aeroelastic effects on pressure distribution as well as total forces and moments. During this design study, the thickness distribution of the wing cover skins was initially sized based on rigid loads and subsequently resized under aeroelastic loads. Comparisons are made between these nonlinear aeroelastic results and results obtained from linear aerodynamic methods applied to a rigid shape during conceptual design studies.

Tatum, Kenneth E.↗

NASA NTRS1986

Variable structure control of nonlinear systems through simplified uncertain models

A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.

Sira-Ramirez, Hebertt↗

NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

NASA NTRS1988

A brief review on the identification of nonlinear mechanical systems

This paper presents a brief review of the disciplines used in the identification of nonlinear mechanical systems, including the detection of nonlinearities and their quantification, and parameter estimation. Techniques for determining the parameters of nonlinear system models with assumed model form are described and briefly discussed. Recent developments in identifying system models which may contain the actual model forms as well as incorrect forms is also briefly described. A list of representative references from structures and control disciplines is given.

Natke, H. G.↗

NASA NTRS1988

A nonlinear analysis of an equilibrium craze. I - Problem formulation and solution. II - Simulations of craze and crack growth

A numerical method is developed for the determinations of the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement behavior. The problem formulation is based on the superposition of the relevant elasticity Green's function; the solution of the resulting nonlinear problem is obtained by using Picard's successive approximation scheme. The model is used to investigate the effect of nonlinear fibril behavior on the mechanics of craze and crack growth, and the results are compared with the Dugdale model.

Ungsuwarungsri, T.↗