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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Bubble and Drop Nonlinear Dynamics (BDND)

Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.

Trinh, E. H.↗
NASA NTRS1983

Nonlinear dynamics and control of a vibrating rectangular plate

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Shebalin, J. V.↗
NASA NTRS1987

Nonlinear dynamics, chaos and complex cardiac arrhythmias

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

Glass, L.↗
NASA NTRS1988

The poststall nonlinear dynamics and control of an F-18: A preliminary investigation

The successful high angle of attack (HAOA) operation of fighter aircraft will necessarily require the introduction of a new onboard control methodology that address the nonlinearity of the system when flown at the stall/poststall limits of the craft's flight envelope. As a precursor to this task, a researcher endeavored to familarize himself with the dynamics of one specific aircraft, the F-18, when it is flown at HAOA. This was accomplished by conducting a number of real time flight sorties using the NASA-Langley Research Center's F-18 simulator, which was operated with a pilot in the loop. In addition to developing a first hand familarity with the aircraft's dynamic characteristic at HAOA, work was also performed to identify the input/output operational footprint of the F-18's control surfaces. This investigator proposes to employ the nonlinear models of the plant identified this summer in a subsequent research effort that will make it possible to fly the F-18 effectively at poststall angles of attack. The controller design used there will rely on a new technique proposed by this investigator that provides for the automatic generation of online optimal control solutions for nonlinear dynamic systems.

Patten, William N.↗
NASA NTRS2000

Simulation of Aircraft Landing Gears with a Nonlinear Dynamic Finite Element Code

Recent advances in computational speed have made aircraft and spacecraft crash simulations using an explicit, nonlinear, transient-dynamic, finite element analysis code more feasible. This paper describes the development of a simple landing gear model, which accurately simulates the energy absorbed by the gear without adding substantial complexity to the model. For a crash model, the landing gear response is approximated with a spring where the force applied to the fuselage is computed in a user-written subroutine. Helicopter crash simulations using this approach are compared with previously acquired experimental data from a full-scale crash test of a composite helicopter.

Lyle, Karen H.↗
NASA NTRS1988

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

Peterson, Lee D.↗
DOE OSTI2016

Nonlinear dynamics induced in a structure by seismic and environmental loading

In this study,we show that under very weak dynamic and quasi-static deformation, that is orders of magnitude below the yield deformation of the equivalent stress strain curve (around 10 -3 ), the elastic parameters of a civil engineering structure (resonance frequency and damping) exhibit nonlinear softening and recovery. These observations bridge the gap between laboratory and seismic scales where elastic nonlinear behavior has been previously observed. Under weak seismic or atmospheric loading, modal frequencies are modified by around 1% and damping by more than 100% for strain levels between 10 -7 and 10 -4 . These observations support the concept of universal behavior of nonlinear elastic behavior in diverse systems, including granular materials and damaged solids that scale from millimeter dimensions to the scale of structures to fault dimensions in the Earth.

58 GEOSCIENCES↗
DOE OSTI2015

X-ray third-order nonlinear dynamical diffraction in a crystal

The dynamic diffraction of an X-ray wave in a crystal with a third-order nonlinear response to external field strength has been theoretically investigated. General equations for the wave propagation in crystal and nonlinear Takagi equations for both ideal and deformed crystals are derived. Integrals of motion are determined for the nonlinear problem of dynamic diffraction. The results of the numerical calculations of reflectivity in the symmetric Laue geometry for an incident plane wave and the intensity distributions on the output crystal surface for a point source are reported as an example.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1991

Nonlinear dynamics near the stability margin in rotating pipe flow

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Yang, Z.↗
DOE OSTI2020

Nonlinear dynamics and dissipation of a curvilinear vortex driven by a strong time-dependent Meissner current

Here, we report numerical simulations of large-amplitude oscillations of a trapped vortex line under a strong ac magnetic field $\textit{H(t) = H}$ sin$\textit{ωt}$ parallel to the surface. The power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was calculated by taking into account the nonlinear vortex line tension, vortex mass, and a nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient $\textit{η(v)}$. We show that the LO decrease of $\textit{η(v)}$ with the vortex velocity $\textit{v}$ can radically change the field dependence of the surface resistance R i ( H ) caused by trapped vortices. At low frequencies, $R_i(H)$ exhibits a conventional increase with $\textit{H}$, but as $\textit{ω}$ increases, the surface resistance becomes a nonmonotonic function of $\textit{H}$ which decreases with $\textit{H}$ at higher fields. The effects of frequency, pin spacing, and the mean-free path $l_i$ on the field dependence of $R_i(H)$ were calculated. It is shown that, as the surface gets dirtier and $l_i$ decreases, the anomalous drop of $R_i(H)$ with $\textit{H}$ shifts to lower fields which can be much smaller than the lower critical magnetic field. Our numerical simulations also show that the LO decrease of $\textit{η(v)}$ with $\textit{v}$ can cause a vortex bending instability at high field amplitudes and frequencies, giving rise to the formation of dynamic kinks along the vortex. Measurements of $R_i(H)$ caused by sparse vortices trapped perpendicular to the surface can offer opportunities to investigate an extreme nonlinear dynamics of vortices driven by strong current densities up to the depairing limit at low temperatures. The behavior of $R_i(H)$, which can be tuned by varying the rf frequency or concentration of nonmagnetic impurities, is not masked by strong heating effects characteristic of dc or pulse transport measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Nonlinear dynamics of combustor azimuthal modes: Experiments and modeling

This paper provides an experimental and theoretical investigation of azimuthal instabilities in a lean, premixed combustor. It presents data from a high Reynolds number, industrial-scale facility with multiple fuel stages that enable variation of radial and azimuthal symmetries. The combustor exhibits a variety of behaviors – including standing, spinning, mixed waves, and intermittent behaviors, as well as periodic limit cycles and quasi-periodic oscillations – depending upon varying power and azimuthal symmetry. A second key objective of this paper is to present a weakly nonlinear framework that is used to understand and interpret these results, showing the influence of eigenmode degeneracy, background noise, and azimuthal non-uniformities in mean quantities such as temperature and flame-acoustic coupling. In particular, this analysis shows the importance of the linear instability growth/damping rate and azimuthal non-uniformities in controlling the relative prominence of standing, spinning, or mixed waves at the limit cycle, as well as the preference in the spinning direction. It also shows the conditions under which single frequency or quasi-periodic oscillations are dominant, and how these are more fundamentally influenced by azimuthal non-uniformities and background noise.

42 ENGINEERING↗
DOE OSTI2023

Nonlinear dynamics of small-scale Alfvén waves

Herein we study the nonlinear evolution of very oblique small-scale Alfvén waves with k ⊥ d i ≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k ⊥ d i ~1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k ⊥ ρ s , k ⊥ d e , or k ∥ d i becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than d i . We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Nonlinear dynamics of quadratic gravity in spherical symmetry

We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (quadratic gravity) in the spherically-symmetric sector. The formulation relies on (i) the harmonic gauge to cast the evolution system into quasilinear form (ii) the Cartoon method to reduce to spherical symmetry in keeping with the harmonic gauge, and (iii) order reduction to first order (in time) by means of introducing auxiliary variables. The well posedness of the respective initial-value problem is numerically confirmed by evolving randomly perturbed flat-space and black-hole initial data. In conclusion, our study serves as a proof-of-principle for the possibility of stable numerical evolution in the presence of higher derivatives.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians

In this paper we propose a new Koopman operator approach for nonlinear model decomposition using Koopman gramians. We introduce Koopman operators and discuss the notion of a input-Koopman operator. We show how input-Koopman operators can be used to cast a nonlinear system into the classical state-space form, as well as conditions under which input and state observable functions are well separated. We extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition, for systems with control or disturbances. We illustrate the accuracy of the method on learning an input-state separable Koopman operator for an example system, even when the underlying system exhibits mixed state-input terms. Finally, we introduce a nonlinear decomposition algorithm, based on Koopman gramians, that maximizes internal subsystem observability and disturbance rejection from unwanted noise in other subsystems. To relieve the NP-hardness of the decomposition problem, we derive a relaxation based on Koopman gramians and multi-way partitioning. We illustrate our algorithm on a swing dynamics model for a IEEE 39 bus and discuss our findings.

Learning, Control, Distributed Control, koopman op↗
DOE OSTI2023

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

A simple model describing the nonlinear dynamics of the dusk/dawn asymmetry in the high-latitude thermospheric flow

A simple nonlinear, axisymmetric, shallow-water numerical model has been used to study the asymmetry in the neutral flow between the dusk and dawn sides of the auroral oval. The results indicate that the Coriolis force and the curvature terms are nearly in balance on the evening side and require only a small pressure gradient to effect adjustment. The result is smaller neutral velocities near dawn and larger velocities near dusk than would be the case for a linearized treatment. A consequence is that more gravity wave energy is produced on the morning side than on the evening side.

Gundlach, J. P.↗
NASA NTRS1994

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

Murthy, V. R.↗