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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

Lin, Ray-Quing↗
NASA NTRS2008

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Cantrell, John H., Jr.↗
NASA NTRS1989

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Buttrill, Carey S.↗
NASA NTRS1991

Correlation techniques to determine model form in robust nonlinear system realization/identification

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Stry, Greselda I.↗
NASA NTRS1982

VLF wave growth and discrete emission triggering in the magnetosphere - A feedback model

A simple nonlinear feedback model is presented to explain VLF wave growth and emission triggering observed in VLF transmission experiments. The model is formulated in terms of the interaction of electrons with a slowly varying wave in an inhomogeneous medium as in an unstable feedback amplifier with a delay line; constant frequency oscillations are generated on the magnetic equator, while risers and fallers are generated on the downstream and upstream sides of the equator, respectively. Quantitative expressions are obtained for the stimulated radiation produced by energy exchanged between energetic electrons and waves by Doppler-shifted cyclotron resonance, and feedback between the stimulated radiation and the phase bunched currents is incorporated in terms of a two-port discrete time model. The resulting model is capable of explaining the observed temporal growth and saturation effects, phase advance, retardation or frequency shift during growth in the context of a single parameter depending on the energetic particle distribution function, as well as pretermination triggering.

Helliwell, R. A.↗
NASA NTRS1992

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Hanson, R. J.↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Deterministic modeling of hybrid nonlinear effects in epsilon-near-zero thin films

In nonlinear optics, significant effort is concentrated on improving the strength and efficiency of interactions; however, experimentally investigating nonlinear materials is a complex, time-consuming, and costly investment. Moreover, it is often challenging to isolate, study, and optimize material parameters in an experiment due to complexities in the growth process. Recently, epsilon-near-zero materials have received a great deal of attention as promising nonlinear optical materials, but like many up-and-coming materials, the ability to explore and optimize their properties has been challenging. Here, we establish a framework to rapidly evaluate the performance of nonlinear epsilon-near-zero materials for both inter- and intraband effects in silico, requiring only an energy-momentum (E-k) diagram, linear optical properties, and experimental conditions. Measured nonlinear reflection and transmission in gallium-doped zinc oxide films are compared to the numerical framework for both intra- and interband excitation to verify accuracy across wavelength and irradiance while two figures of merit (FoMs) are introduced to quickly evaluate the performance of films without a full numerical framework. This capability is used to predict the performance of highly doped gallium nitride, cadmium oxide, zinc oxide, and indium tin oxide films, and efficient intra- and interband operation conditions are identified. Through this numerical framework and the FoMs, the exploration of unstudied epsilon-near-zero materials is enabled without the need for a nonlinear experiment, thereby accelerating the search for more efficient nonlinear materials and excitation conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2017

Propulsion Controls Modeling for a Small Turbofan Engine

A nonlinear dynamic model and propulsion controller are developed for a small-scale turbofan engine. The small-scale turbofan engine is based on the Price Induction company's DGEN 380, one of the few turbofan engines targeted for the personal light jet category. Comparisons of the nonlinear dynamic turbofan engine model to actual DGEN 380 engine test data and a Price Induction simulation are provided. During engine transients, the nonlinear model typically agrees within 10 percent error, even though the nonlinear model was developed from limited available engine data. A gain scheduled proportional integral low speed shaft controller with limiter safety logic is created to replicate the baseline DGEN 380 controller. The new controller provides desired gain and phase margins and is verified to meet Federal Aviation Administration transient propulsion system requirements. In understanding benefits, there is a need to move beyond simulation for the demonstration of advanced control architectures and technologies by using real-time systems and hardware. The small-scale DGEN 380 provides a cost effective means to accomplish advanced controls testing on a relevant turbofan engine platform.

jet propulsion↗
NASA NTRS1983

On the analytical modeling of the nonlinear vibrations of pretensioned space structures

Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.

Housner, J. M.↗
DOE OSTI2023

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response

Here we demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation–dissipation method for water and acetonitrile. We examine this method’s trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Measuring signatures in photon angular spectra to distinguish nonlinear Compton scattering models

The collision of a high-energy electron beam with a laser pulse may be used to study radiation reaction and nonlinear Compton scattering among many other processes in strong-field quantum electrodynamics. Predictions from simulation and theory for these interactions rely on a number of approximations and assumptions that have not been experimentally tested. Here, experimentally measurable signatures are identified that might be able to distinguish between radiation reaction models, i.e., classical or quantum, or between the local constant field and local monochromatic approximations used to calculate the properties of the nonlinear Compton process. These signatures are considered through Monte Carlo simulations of various experimental conditions that are relevant to today's laser facilities. Potential detection schemes for measuring the signatures are proposed. We find that single-photon counting of keV photons to resolve harmonics and scintillator-based detection of MeV photons may allow us to validate nonlinear Compton scattering models and radiation reaction models respectively. This will require electron beams with divergence angles less than 2 mrad and less than 20% energy spread.

Russell, Brandon K↗
NASA NTRS1996

Nonlinear Analysis and Modeling of Tires

The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.

Noor, Ahmed K.↗
DOE OSTI2022

Effect of injected flux and current temporal phasing on self-organization in the HIT-SI3 experiment

The HIT-SI3 device at the University of Washington uses three oscillating inductive helicity injectors to form and sustain spheromak plasma equilibria. By adjusting the temporal phase of the injector waveforms with respect to each other, the toroidal spectrum of the imposed perturbations can be controlled. Using a recently implemented GPU-based control system, the available mode spectra were explored experimentally by scanning the space of relative injector phasing. In this space, significant variation in the toroidal mode spectrum ($n$ = 1, 2, 3) of the perturbations was observed. Additionally, variation in characteristics of driven equilibria was also observed, including a ≈ $30$% range in toroidal current gain ($I$ $Φ$ / $I$ $Inj$ ). Experimental results are compared with both a composite-equilibria and nonlinear dynamic model, including extended MHD simulations using the NIMROD code and composite Taylor state equilibria computed using the PSI-Tet code. In conclusion, qualitative agreement is seen with the nonlinear models, but not with composite-equilibria models, suggesting the use of nonlinear models to better capture observed plasma dynamics and provide predictive use for future experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

Effects of nonlinear damping in flexible space structures

The classical Krylov-Bogoliubov "averaging" technique is used to study a class of nonlinear damping models, for which the damping force is proportional to the product of positive integer or fractional power of absolute values of displacement and that of velocity. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on damping ratio, but also on the initial amplitude, the time to measure the response, frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce energy of the system as well as to pass energy to higher modes. Experimental evidence such as in Spacecraft Control Laboratory Experiment seems to support the need for nonlinear models.

Hu, Anren↗
DOE OSTI2021

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Here, we report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

42 ENGINEERING↗
NASA NTRS1985

Nonlinear finite element models of laminated plates and shells

In this expository paper a first-order shear deformation laminate theory that accounts for the von Karman strains is described and its finite element model is developed. The element also accounts for Hill's elastic-perfectly plastic material model. Sample applications of the present element to linear and nonlinear bending of laminated plates and shells are presented. Numerical results showing the effects of boundary conditions, lamination scheme, and loading on the deflections and stresses are also presented. It is found that the effect of shear deformation and boundary conditions on deflections are significant.

Redddy, J. N.↗