A high-order perturbation theory using rectangular coordinates.
Runge-kutta integration to approximate system of nonlinear equations by series of linear equations
RUNGE-KUTTA INTEGRATION↗
SEARCH · Engineering Papers
Results for “nonlinear mechanics”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Evaluation of Inelastic Constitutive Models for Nonlinear Structural Analysis
The influence of inelastic material models on computed stress-strain states, and therefore predicted lives, was studied for thermomechanically loaded structures. Nonlinear structural analyses were performed on a fatigue specimen which was subjected to thermal cycling in fluidized beds and on a mechanically load cycled benchmark notch specimen. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic-kinematic, combined plus transient creep) were exercised. Of the plasticity models, kinematic hardening gave results most consistent with experimental observations. Life predictions using the computed strain histories at the critical location with a Strainrange Partitioning approach considerably overpredicted the crack initiation life of the thermal fatigue specimen.
Kaufman, A.↗
Computer studies of baroclinic flow
Programs necessary for computing the transition curve on the regime diagram for the atmospheric general circulation experiment (AGOE) were completed and used to determine the regime diagram for the rotating annulus and some axisymmetric flows for one possible AGOE configuration. The effect of geometrical constraints on the size of eddies developing from a basic state is being examined. In AGOE, the geometric constraint should be the width of the shear zone or the baroclinic zone. Linear and nonlinear models are to be used to examine both barotropic and baroclinic flows. The results should help explain the scale selection mechanism of baroclinic eddies in the atmosphere experimental models such as AGOE, and the multiple vortex phenomenon in tornadoes.
Gall, R.↗
Selfsimilar time dependent shock structures
Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The ame argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions.
Beck, R.↗
Induced emission of radiation near 2(omega sub e) by a synchrotron-maser instability
In the literature, the emission of radiation at 2(omega sub e), where omega sub e denotes the electron plasma frequency, is usually explained as having been produced by the nonlinear interaction of two Langmuir waves via a backscattering process. Since the emission is frequently observed in solar radio bursts, the mechanism has attracted considerable theoretical interest. In the present paper a model is proposed based on a synchrotron-maser instability excited by a hollow beam of moderately relativistic electrons in a plasma, in which the plasma frequency is much higher than the gyrofrequency. An important conclusion is that, as a result of this instability, unpolarized electromagnetic waves with frequencies near 2(omega sub e) may be amplified.
Wu, C. S.↗
Modeling and control design of a wind tunnel model support
The 12-Foot Pressure Wind Tunnel at Ames Research Center is being restored. A major part of the restoration is the complete redesign of the aircraft model supports and their associated control systems. An accurate trajectory control servo system capable of positioning a model (with no measurable overshoot) is needed. Extremely small errors in scaled-model pitch angle can increase airline fuel costs for the final aircraft configuration by millions of dollars. In order to make a mechanism sufficiently accurate in pitch, a detailed structural and control-system model must be created and then simulated on a digital computer. The model must contain linear representations of the mechanical system, including masses, springs, and damping in order to determine system modes. Electrical components, both analog and digital, linear and nonlinear must also be simulated. The model of the entire closed-loop system must then be tuned to control the modes of the flexible model-support structure. The development of a system model, the control modal analysis, and the control-system design are discussed.
Howe, David A.↗
Regolith-structure modeling of lunar facilities
The mechanical properties of lunar regolith are significantly different from terrestrial soils; at low stress levels, the ultimate strength envelope is highly nonlinear, and the material is essentially dilatant. The effects of platen friction, membrane confinement, and material self weight in triaxial tests have been shown to be of great significance in low stress level tests. An inverse identification technique has been devised to account for these effects where the load-displacement response of the entire specimen, including the boundary conditions and the self-weight, was analyzed by nonlinear finite element techniques so as to obtain true material parameters.
Perkins, Steven W.↗
Modeling and control design of a wind tunnel model support
The 12-Foot Pressure Wind Tunnel at Ames Research Center is being restored. A major part of the restoration is the complete redesign of the aircraft model supports and their associated control systems. An accurate trajectory control servo system capable of positioning a model (with no measurable overshoot) is needed. Extremely small errors in scaled-model pitch angle can increase airline fuel costs for the final aircraft configuration by millions of dollars. In order to make a mechanism sufficiently accurate in pitch, a detailed structural and control-system model must be created and then simulated on a digital computer. The model must contain linear representations of the mechanical system, including masses, springs, and damping in order to determine system modes. Electrical components, both analog and digital, linear and nonlinear must also be simulated. The model of the entire closed-loop system must then be tuned to control the modes of the flexible model-support structure. The development of a system model, the control modal analysis, and the control-system design are discussed.
Howe, David A.↗
Program For Analysis Of Metal-Matrix Composites
METCAN (METal matrix Composite ANalyzer) is computer program used to simulate computationally nonlinear behavior of high-temperature metal-matrix composite structural components in specific applications, providing comprehensive analyses of thermal and mechanical performances. Written in FORTRAN 77.
Murthy, P. L. N.↗
Dynamic interpretation of space shuttle photographs: Deepwater internal waves in the western equatorial Indian Ocean
Visible images of deep-ocean internal waves in the western equatorial Indian Ocean taken by the space shuttle Atlantis during mission STS 44 in 1991 are interpreted and analyzed. The internal waves occurred in the form of a multisoliton packet in which there are about a dozen solitons. The average wavelength of the solitons is 1.8 +/- 0.5 km, ranging from 1.1 to 2.6 km. The crest lines are mostly straight and reach as long as 100 km. The distance between two adjacent packets is about 66 km. Using the deepwater soliton theory, we derived that the mean amplitude of the solitons is 25 m, the nonlinear phase speed is 1.7 m/s, and the average period is 18 min. The internal semidiurnal tides are the principal generating mechanism. The oblique collision of two multisoliton packets shown on photograph STS 44-93-103 is examined. The results show that the deep-ocean internal waves obey the general properties of soliton collision. The leading solitons and a few followers exhibit some properties of inelastic collision characterized by a phase shift, and the rest of the solitons exhibits properties of elastic collision under resonance conditions.
Zheng, Quanan↗
Application of Space Shuttle photography to studies of upper ocean dynamics
Three studies have been conducted using space shuttle imagery to explain the dynamics behavior of internal waves in the Atlantic and Indian Oceans and to derive tide-related parameters for Delaware Bay. By interpreting space shuttle photographs taken during mission STS-40, a total of 34 internal wave packets on the continental shelf of the Middle Atlantic Bight have been recognized. Using the finite-depth theory we derived that the maximum amplitude of solitons is 5.6 m, the phase speed 0.42 m/s, and the period 23.8 min. Deep-ocean internal waves in the western equatorial Indian Ocean on photographs taken during mission STS-44 were also interpreted and analyzed. The internal waves occurred in the form of a multisoliton packet in which there are about a dozen solitons. The average wavelength of the solitons is 1.8 +/- 0.5 km. The crest lines are mostly straight and reach as long as 100 km. The distance between two adjacent packets is about 66 km. Using the deepwater soliton theory, we derived that the mean amplitude of the solitons is 25 m, the nonlinear phase speed 1.7 m/s, and the average period 18 min. For both cases, the semidiural tides are the principal generating mechanism. The tide-related parameters of Delaware Bay were derived from space shuttle time-series photographs taken during mission STS-40. The water area in the bay were measured from interpretation maps of the photographs. The corresponding tidal levels were calculated using the exposure time. From these data, an approximate function relating the water area to the tidal level at a reference point was determined. Then, the water areas of the Delaware Bay at mean high water (MHW) and mean low water (MLW), below 0 m, for the tidal zone, and the tidal flux were inferred. All parameters derived were reasonable and compared well with results of previous investigations.
Zheng, Quanan↗
[Kelvin-Helmholtz instability in protostellar jets]
NASA grant NAG 5 2866, funded by the Astrophysics Theory Program, enabled the study the Kelvin-Helmholtz instability in protostellar jets. In collaboration with co-investigator Philip Hardee, the PI derived the analytic dispersion relation for the instability in including a cooling term in the energy equation which was modeled as one of two different power laws. Numerical solutions to this dispersion relation over a wide range of perturbation frequencies, and for a variety of parameter values characterizing the jet (such as Mach number, and density ratio) were found It was found that the growth rates and wavelengths associated with unstable roots of the dispersion relation in cooling jets are significantly different than those associated with adiabatic jets, which have been studied previously. In collaboration with graduate student Jianjun Xu (funded as a research associate under this grant), hydrodynamical simulations were used to follow the growth of the instability into the nonlinear regime. It was found that asymmetric surface waves lead to large amplitude, sinusoidal distortions of the jet, and ultimately to disruption Asymmetric body waves, on the other hand, result in the formation of shocks in the jet beam in the nonlinear regime. In cooling jets, these shocks lead to the formation of dense knots and filaments of gas within the jet. For sufficiently high perturbation frequencies, however, the jet cannot respond and it remains symmetric. Applying these results to observed systems, such as the Herbig-Haro jets HH34, HH111 and HH47 which have been observed with the Hubble Space Telescope, we predicted that some of the asymmetric structures observed in these systems could be attributed to the K-H modes, but that perturbations on timescales associated with the inner disk (about 1 year) would be too rapid to cause disruption. Moreover, it was discovered that weak shock 'spurs' in the ambient gas produced by ripples in the jet surface due to nonlinear, modes of surface and/or body waves could accelerate the ambient gas to low velocity. This latter effect represents a new mechanism by which supersonic jets can accelerate low velocity outflows.
Stone, James↗
Fabrication and Characterization of Thin Film Ion Implanted Composite Materials for Integrated Nonlinear Optical Devices
Ion implantation has been shown to produce a high density of metal colloids within the layer regions of glasses and crystalline materials. The high-precipitate volume fraction and small size of metal nanoclusters formed leads to values for the third-order susceptibility much greater than those for metal doped solids. This has stimulated interest in use of ion implantation to make nonlinear optical materials. On the other side, LiNbO3 has proved to be a good material for optical waveguides produced by MeV ion implantation. Light confinement in these waveguides is produced by refractive index step difference between the implanted region and the bulk material. Implantation of LiNbO3 with MeV metal ions can therefore result into nonlinear optical waveguide structures with great potential in a variety of device applications. We describe linear and nonlinear optical properties of a waveguide structure in LiNbO3-based composite material produced by silver ion implantation in connection with mechanisms of its formation.
Sarkisov, S.↗
Characterization of Composites Response at High Rates of Loading
The objective of the proposed research is to experimentally study the effect of strain rate on mechanical response (deformation and failure) carbon fiber/epoxy matrix composites. The experimental data provide the information needed for the development of a nonlinear, rate dependent deformation and strength models that can subsequently be used in design. This year effort was directed into testing the epoxy resin. Two types of epoxy were tested each in tension and shear at various strain rate that ranges from 5x10(exp -5), to 700/s. The results show that both the strain rate and the mode of loading affect the epoxy response.
Gilat, Amos↗
Minnowbrook I: 1993 Workshop on End-Stage Boundary Layer Transition
This volume contains materials presented at the Minnowbrook I-1993 Workshop on End-Stage Boundary Layer Transition, held at the Syracuse University Minnowbrook Conference Center, New York, from August 15 to 18, 1993. This volume was previously published as a Syracuse University report edited by John E. LaGraff. The workshop organizers were John E. LaGraff (Syracuse University), Terry V. Jones (Oxford University), and J. Paul Gostelow (University of Technology, Sydney). The workshop focused on physical understanding of the late stages of transition from laminar to turbulent flows, with the specific goal of contributing to improving engineering design of turbomachinery and wing airfoils. The workshop participants included academic researchers from the United States and abroad, and representatives from the gas-turbine industry and U.S. government laboratories. To improve interaction and discussions among the participants, no formal papers were required. The physical mechanisms discussed were related to natural and bypass transition, wake-induced transition, effects of freestream turbulence, turbulent spots, hairpin vortices, nonlinear instabilities and breakdown, instability wave interactions, intermittency, turbulence, numerical simulation and modeling of transition, heat transfer in boundary-layer transition, transition in separated flows, laminarization, transition in turbomachinery compressors and turbines, hypersonic boundary-layer transition, and other related topics. This volume contains abstracts and copies of the viewgraphs presented, organized according to the workshop sessions. The workshop summary and the plenary discussion transcript clearly outline future research needs.
LaGraff, John E.↗
Modeling Fiber Kinking at the Microscale and Mesoscale
A computational micromechanics (CMM) model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking. The CMM model considers an individually discretized three dimensional fiber and surrounding matrix accounting for nonlinearity in the fiber, matrix plasticity, fiber/matrix interface debonding, and geometric nonlinearity. Key parameters of the CMM model were measured through experiments. In particular, a novel experimental technique to characterize the in situ longitudinal compressive strength of carbon fibers through indentation of micropillars is presented. The CDM model is formulated on the basis of Budiansky's fiber kinking theory (FKT) with a constitutive deformation-decomposition approach to alleviate mesh size sensitivity. In contrast to conventional mesoscale CDM models that prescribe a constitutive response directly, the response of the proposed model is an outcome of material nonlinearity and large rotations of the fiber direction following FKT. Comparison of the predictions from the CMM and CDM models shows remarkable correlation in strength, post-peak residual stress, and fiber rotation, with less than 10% difference between the two models in most cases. Additional comparisons are made with several fiber kinking models proposed in the literature to highlight the efficacy of the two models. Finally, the CMM model is exercised in parametric studies to explore opportunities to improve the longitudinal compression strength of a ply through the use of nonconventional microstructures.
Herraez, Miguel↗
Computer simulation of multiple pilots flying a modern high performance helicopter
A computer simulation of a human response pilot mechanism within the flight control loop of a high-performance modern helicopter is presented. A human response mechanism, implemented by a low order, linear transfer function, is used in a decoupled single variable configuration that exploits the dominant vehicle characteristics by associating cockpit controls and instrumentation with specific vehicle dynamics. Low order helicopter models obtained from evaluations of the time and frequency domain responses of a nonlinear simulation model, provided by NASA Lewis Research Center, are presented and considered in the discussion of the pilot development. Pilot responses and reactions to test maneuvers are presented and discussed. Higher level implementation, using the pilot mechanisms, are discussed and considered for their use in a comprehensive control structure.
Zipf, Mark E.↗
A 6 degree-of-freedom Lorentz force vibration isolator with nonlinear controller
This program demonstrated the technical feasibility of constructing large-stroke magnetic suspensions that can meet the active vibration isolation requirements of Space Station. These requirements include: (1) strokes over 1 cm in all directions, (2) actuator bandwidths over 100 Hz, (3) isolator roll-off frequencies below 10(exp -2) Hertz, and (4) force capability over 1 Newton in all axes. The 100 Hz actuator bandwidth allows the suspension to reject any direct force disturbances that act on the microgravity experiment, for example forces created by cable connections. The low isolator roll-off frequency and large stroke allow the magnetic suspension to isolate the microgravity experiment from Space Station vibrations above the roll-off frequency. The capability to meet these requirements was demonstrated by designing, constructing and testing a six-degree-of-freedom, prototype magnetic suspension system that featured high-performance, Lorentz-force actuators and full multi-input, multi-output control. This prototype suspension is designed to isolate large orbiter locker experiments under typical spacecraft constraints of size, weight, and power. Suspension in the full six-degrees-of-freedom was successfully demonstrated in this program while using a gravity-force unload mechanism to simulate a space environment. The prototype isolator is capable of space-based isolation service with relatively minor modification. The use of advanced, nonlinear control algorithms were investigated on a specially designed single-degree-of-freedom testbed. This low acceleration test facility simulates the Space Station vibration isolation problem in a single horizontal axis with low-friction, air-slide support. This allowed testing at the desired microgravity levels, without the gravity bias effects that are seen in a full six-degrees-of-freedom suspension. Precision components were used to reduce residual accelerations to microgravity levels so that the effects of sensor, actuator, and electronic noise could be evaluated. During the Phase 2 program, this testbed was used to demonstrate the advantages of nonlinear control algorithms to provide increased vibration isolation performance.
Fenn, Ralph↗