Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear response”

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.

At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak

According to a recent paper [Hu et al ., Phys. Plasmas 26, 120702 (2019)], mode penetration at the top of the pedestal is a necessary and sufficient condition for the suppression of edge localized modes (ELMs) by a resonant magnetic perturbation (RMPs) in an H-mode tokamak discharge. This paper employs asymptotic matching theory to model a particular DIII-D discharge in which ELMs were suppressed by an externally generated, static, n ¼ 2, RMP whose amplitude was modulated at a frequency of 1 Hz. It is demonstrated that the response of the plasma to the applied RMP, in the immediate vicinities of the rational (i.e., resonant) surfaces, is governed by nonlinear, rather than by linear, physics. This is the case because the magnetic island widths associated with driven reconnection exceed the linear layer widths, even in cases where driven reconnection is strongly suppressed by plasma rotation. The natural frequency at a given rational surface (i.e., the helical frequency at which the locally resonant component of the RMP would need to propagate in order to maximize driven reconnection) is found to be offset from the local E B frame in the ion diamagnetic direction. The size of the offset is mostly determined by neoclassical poloidal rotation. Finally, the predictions of a fully nonlinear plasma response model are found to be broadly consistent with the DIII-D experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1980

Jump phenomena

The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

Reiss, E. L.↗
NASA NTRS1988

Linear response theory for annealing of radiation damage in semiconductor devices

A theoretical study of the radiation/annealing response of MOS ICs is described. Although many experiments have been performed in this field, no comprehensive theory dealing with radiation/annealing response has been proposed. Many attempts have been made to apply linear response theory, but no theoretical foundation has been presented. The linear response theory outlined here is capable of describing a broad area of radiation/annealing response phenomena in MOS ICs, in particular, both simultaneous irradiation and annealing, as well as short- and long-term annealing, including the case when annealing is nearing completion. For the first time, a simple procedure is devised to determine the response function from experimental radiation/annealing data. In addition, this procedure enables us to study the effect of variable temperature and dose rate, effects which are of interest in spaceflight. In the past, the shift in threshold potential due to radiation/annealing has usually been assumed to depend on one variable: the time lapse between an impulse dose and the time of observation. While such a suggestion of uniformity in time is certainly true for a broad range of radiation annealing phenomena, it may not hold for some ranges of the variables of interest (temperature, dose rate, etc.). A response function is projected which is dependent on two variables: the time of observation and the time of the impulse dose. This dependence on two variables allows us to extend the theory to the treatment of a variable dose rate. Finally, the linear theory is generalized to the case in which the response is nonlinear with impulse dose, but is proportional to some impulse function of dose. A method to determine both the impulse and response functions is presented.

Litovchenko, Vitaly↗
NASA NTRS1991

Non-linear dynamics of a geared rotor-bearing system with multiple clearances

The nonlinear frequency response characteristics of a geared rotor-bearing system are examined. A three-DOF dynamic model is developed which includes nonlinearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The applicability of both analytical and numerical solution techniques to the multi-DOF nonlinear problem is investigated. Satisfactory agreement is found between the theory presented here and the available experimental data. Nonlinear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. In addition, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the nonlinear dynamic behavior.

Kahraman, A.↗
DOE OSTI2024

An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

An optimization-based design framework is proposed to tune the response of soft metamaterials involving both geometric instabilities and nonlinear viscoelastic material behavior. Designing the response of soft metamaterials to harness instabilities and undergo large, tailored configuration changes will enable advancements in soft robotics, shock and vibration mitigation, and flexible electronics. In line with the metamaterial concept, the response of these materials is governed to a large extent by the geometric and topological makeup of their small-scale features. However, the link between structure and response is less intuitive for soft metamaterials due to their reliance upon highly nonlinear responses triggered by geometric instabilities. This is further complicated by the effects of viscoelastic relaxation, which recent studies have shown to alter the emergence of instabilities in non-intuitive ways. Here, these effects are accounted for in our framework to achieve various design objectives, including tailored force–displacement response and maximized energy absorption from both geometric and material effects. To fully automate this process, it is essential to have a completely robust equation solver for forward problems involving instabilities and viscoelastic relaxation. We achieve this by casting the search for stable mechanical equilibrium — i.e. the forward problem — as a minimization problem and utilize a trust region algorithm to robustly handle instabilities and follow energetically-favorable equilibrium paths through critical points.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Some inconsistencies of the finite element method as applied to inelastic response

The inadequacy of a two noded beam-column element with a linear axial and a cubic transverse displacement field for inelastic analysis is demonstrated. For complete equilibrium satisfaction in the linear elastic range a three noded beam-column element is shown to be consistent. Next, the sensitivity of the inelastic response to numerical solutions of the inelastic response of a cantilever beam resulting from approximate integration of strain energy are brought out and finally, consequences of this on the nonlinear transient response of structures are considered.

Kamat, M. P.↗
NASA NTRS2019

The Salience of Nonlinearities in the Boreal Winter Response to ENSO: Arctic Stratosphere and Europe

The Arctic stratospheric response to El Niño (EN) and La Niña (LN) is evaluated in a 41 member ensemble of the period 1980 to 2009 in the Goddard Earth Observing System Chemistry-Climate Model. We consider whether the responses to EN and LN are equal in magnitude and opposite in sign, whether the responses to moderate and extreme events are proportion-ate, and if the response depends on whether sea surface temperature anomalies (SSTs) peak in the Eastern Pacific (EP) or Central Pacific (CP). There is no indication of any nonlinearities between EN and LN, though in ~ 15% of the ensemble members the stratospheric sudden warming (SSW) frequencies for EN and LN are similar, suggesting that a similar SSW frequency for EN and LN, as has occurred over the past ~ 60 years, can occur by chance. The response to extreme EN events is not proportionate to the amplitude of the underlying SST anomalies in spring. EP EN events preferentially increase zonal wavenumber 1 and decrease zonal wavenumber 2 as compared to CP EN events, however the zonal-mean Arctic stratospheric and subpolar surface response is generally little different between EP EN and CP EN once one accounts for the relative weakness of CP events. These differences between EP and CP events and between moderate and extreme EN events only emerge if at least 25 events are composited, however, due to the small signal-to-noise ratio, and hence these differences may be of little practical benefit.

Sea surface temperature anomalies (SSTs) peak in t↗
NASA NTRS1986

Temperature dependent nonlinear metal matrix laminae behavior

An analytical method is described for computing the nonlinear thermal and mechanical response of laminated plates. The material model focuses upon the behavior of metal matrix materials by relating the nonlinear composite response to plasticity effects in the matrix. The foundation of the analysis is the unidirectional material model which is used to compute the instantaneous properties of the lamina based upon the properties of the fibers and matrix. The unidirectional model assumes that the fibers properties are constant with temperature and assumes that the matrix can be modelled as a temperature dependent, bilinear, kinematically hardening material. An incremental approach is used to compute average stresses in the fibers and matrix caused by arbitrary mechanical and thermal loads. The layer model is incorporated in an incremental laminated plate theory to compute the nonlinear response of laminated metal matrix composites of general orientation and stacking sequence. The report includes comparisons of the method with other analytical approaches and compares theoretical calculations with measured experimental material behavior. A section is included which describes the limitations of the material model.

Barrett, D. J.↗
DOE OSTI2023

Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems

Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.

42 ENGINEERING↗
NASA NTRS1995

Nonlinear vibrations of thin-walled composite frames

A reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of thin-walled composite frames. The sensitivity coefficients are the derivatives of the nonlinear frequency with respect to the material and lamination parameters of the frame. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The flanges and webs of the frames are modeled by using geometrically nonlinear two-dimensional shell and plate finite elements. The computational procedure can be conveniently divided into three distinct steps. The first step involves the generation of various-order perturbation vectors, and their derivatives with respect to the material and lamination parameters of the frame, using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation vectors as basis vectors, computing the amplitudes of these vectors and the nonlinear frequency of vibration, via a direct variational procedure. The third step consists of using the perturbation vectors, and their derivatives, as basis vectors and computing the sensitivity coefficients of the nonlinear frequency via a second application of the direct variational procedure. Numerical results are presented for semicircular thin-walled frames with I and J section, showing the convergence of the nonlinear frequency and the sensitivity coefficients obtained by both the reduced-basis and perturbation techniques.

Noor, Ahmed K.↗
NASA NTRS1986

Output time response approximation

The approximation of the output response of a nonlinear system by the output response of a linear system to a desired order irrespective of the admissible input applied should prove useful for purposes of control generation and simulation. Given a nonlinear system, an integer k, and an open subset of state space, sufficient conditions are stated that such a linear approximation exists to order k for every point in the set. In addition, a method for finding the approximating linear systems is presented.

Hunt, L. R.↗
DOE OSTI2020

Room Temperature Quasi-static Characterization and Constitutive Model Parametrization of Flexible Polyurethane Foams of Different Densities Loaded in Different Orientations

This report describes the efforts to characterize and model General Plastics TF6070 and EF4000 flexible polyurethane foams under room temperature, large deformation quasi-static cyclic mechanical loading conditions. Densities from three to fifteen pound per cubic foot (PCF) are examined, which correspond to relative densities of approximately 4 to 20%. These foams are open cell structured and flexible at room temperature with a glass transition transition less than -30°C, and they fully recover their original shape when unloaded (at room temperature). Uniaxial compression tests were conducted with accompanying lateral image series for Digital Image Correlation (DIC) analysis with the goal of extracting transverse strain responses. Due to difficulties with DIC analysis at large strains, lateral strains were instead extracted for each test via edge tracking. The experimental results exhibit a nonlinear elastic response and anisotropic material behavior (particularly for the lower densities). Some hysteresis is observed that is different between the first and subsequent cycles of deformation indicating both a small degree of permanent damage (reduced stiffness during reloading) and viscoelasticity. These inelastic mechanisms are not considered in the modeling and calibration in this report. This work considers only the rate independent, room temperature foam behavior. Individual foam densities were calibrated for loading in two directions, parallel and perpendicular to the foam bubble rise direction, since the mechanical behavior is different in these two directions. The Flex Foam constitutive model was used for all parameterizations despite the fact that the model is isotropic. A review of the constitutive model is given as well as necessary data reduction procedures to parameterize it for each foam density and orientation are discussed. Finally, two different parameterizations are developed that take the undeformed foam density as an input that span all densities considered. These two parameterized models represent foams loaded in the rise and transverse directions respectively. We summarize the assumptions and limitations of the parameterizations provided in this report to guide analysis choices with them. All parameterizations presented herein have the following traits, room temperature, rate independent, damage-free, and non-dissipative . Isotropy (even if they are representing anisotropic data). Supplied Sierra Solid Mechanics Flex Foam Model Inputs are in units: pounds, inches, Celsius, and seconds

36 MATERIALS SCIENCE↗
NASA NTRS1989

Assessment of structural analysis technology for elastic shell collapse problems

The prediction of the ultimate load carrying capability for compressively loaded shell structures is a challenging nonlinear analysis problem. Selected areas of finite element technology research and nonlinear solution technology are assessed. Herein, a finite element analysis procedure is applied to four shell collapse problems which have been used by computational structural mechanics researchers in the past. This assessment will focus on a number of different shell element formulations and on different approaches used to account for geometric nonlinearities. The results presented confirm that these aspects of nonlinear shell analysis can have a significant effect on the predicted nonlinear structural response. All analyses were performed using the CSM Testbed software system which allowed a convenient assessment of different element formulations with a consistent approach to solving the discretized nonlinear equations.

Knight, N. F., Jr.↗
NASA NTRS1998

High-Alpha Research Vehicle Lateral-Directional Control Law Description, Analyses, and Simulation Results

This report contains a description of a lateral-directional control law designed for the NASA High-Alpha Research Vehicle (HARV). The HARV is a F/A-18 aircraft modified to include a research flight computer, spin chute, and thrust-vectoring in the pitch and yaw axes. Two separate design tools, CRAFT and Pseudo Controls, were integrated to synthesize the lateral-directional control law. This report contains a description of the lateral-directional control law, analyses, and nonlinear simulation (batch and piloted) results. Linear analysis results include closed-loop eigenvalues, stability margins, robustness to changes in various plant parameters, and servo-elastic frequency responses. Step time responses from nonlinear batch simulation are presented and compared to design guidelines. Piloted simulation task scenarios, task guidelines, and pilot subjective ratings for the various maneuvers are discussed. Linear analysis shows that the control law meets the stability margin guidelines and is robust to stability and control parameter changes. Nonlinear batch simulation analysis shows the control law exhibits good performance and meets most of the design guidelines over the entire range of angle-of-attack. This control law (designated NASA-1A) was flight tested during the Summer of 1994 at NASA Dryden Flight Research Center.

Davidson, John B.↗
DOE OSTI2021

A quantitative assessment of the model form error of friction models across different interface representations for jointed structures

Hysteretic models are widely used to model frictional interactions in joints to recreate experimental behavior. However, it is unclear which models are best suited for fitting or predicting the responses of structures. Here, the present study evaluates 26 friction model/interface representation combinations to quantify the model form error. A Quasi-Static Modal Analysis approach (termed Rayleigh Quotient Nonlinear Modal Analysis) is adopted to calculate the nonlinear system response, and a Multi-Objective Optimization is solved to fit experimental data of the first mode of the Brake-Reuß Beam. Optimized parameters from the first mode are applied to the second and third bending modes to quantify the predictive ability of the models. Formulations for both tracing full hysteresis loops and recreating hysteresis loops from a single loading curve (Masing assumptions) are considered. Smoothly varying models applied to a five patch representation showed the highest flexibility (for fitting mode 1) and good predictive potential (for modes 2 and 3). For a second formulation, which uses 152 frictional elements to represent the interface, the physically motivated spring in series with a Coulomb slip model (elastic dry friction) has high error for fitting mode 1 and performs near the middle for predicting higher modes. For both interface representation, the best fit models are not the most physical, but rather the ones with the most parameters (as expected); however, the more physical models perform somewhat better for predicting the higher modes.

42 ENGINEERING↗
NASA NTRS1986

Unified constitutive materials model development and evaluation for high-temperature structural analysis applications

Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine hot section components with particular application to an isotropic material used for combustor liners. Differential forms of models independently developed were considered in this study. These models combine the interactions of time-dependent (creep) and time-independent (plasticity) inelastic behavior of a material. Predicted stress-strain responses from these models were evaluated against cyclic isothermal and nonisothermal test results for uniaxial specimens of a nickel-base superalloy. The unified models were implemented in a nonlinear structural analysis code. Two unique NASA Lewis test facilities were used in the evaluation of the models for complex geometry specimens and evaluation of advanced temperature and high-temperature strain measurement instrumentation. Predicted nonlinear structural responses from one of the models for a flat plate and a segment of a conventional combustor liner are presented.

Thompson, R. L.↗