Functional analysis of systems characterized by nonlinear differential equations
Functional analysis of nonlinear systems characterized by differential equations
NONLINEAR SYSTEM↗
SEARCH · Search NASA
Results for “nonlinear characterization”
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.
A nonlinear viscoelastic characterization of graphite/epoxy composites
A nonlinear viscoelastic model based on the procedure of Findley et al., (1948) has been used to accurately represent the creep of several graphite/epoxy composites. Applying this approach to unidirectional 0, 90 and 10 deg off-axis tensile specimens, the viscoelastic response of a lamina can be characterized. The resulting lamina model has been useful for representing the behavior of a lamina in a numerical procedure to predict creep and delayed failures of general laminates. Also, independently, the Findley procedure has been used to characterize the nonlinear viscoelastic behavior of general laminates.
Dillard, D. A.↗
Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology
Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.
Strganac, Thomas W.↗
Nonlinear viscoelastic characterization of thin polyethylene film
In order to understand the state of stress and strain in a typical balloon fabricated from thin polyethylene film, experiment data in the literature reviewed. It was determined that the film behaves as a nonlinear viscoelasticity material and should be characterized accordingly. A simple uniaxial, nonlinear viscoelastic model was developed for predicting stress given a certain strain history. The simple model showed good qualitative agreement with results of constant rate, uniaxial accurately predicting stresses for cyclic strain histories typical of balloon flights. A program was outlined which will result in the development of a more complex nonlinear viscoelastic model.
Wilbeck, J. S.↗
Nonlinear viscoelastic characterization of polycarbonate
Uniaxial tensile creep and recovery data from polycarbonate at six temperatures and six stress levels are analyzed for nonlinear viscoelastic constitutive modeling. A theory to account for combined effects of two or more accelerating factors is presented.
Caplan, E. S.↗
Nonlinear Ultrasonic Characterization of Fatigue Microstructures
Dislocation dipole substructures formed during metal fatigue are shown to produce a substantial distortion of ultrasonic waves propagating through the fatigued material. A model of ultrasonic wave-dislocation dipole interactions is developed that quantifies the wave distortion by means of a material nonlinearity parameter (beta). Application of the model to AA2024-T4 predicts a value of p approximately 300% larger in material cyclically loaded for 100 kcycles in stress-control at 276 MPa and R=0 than that measured for virgin material. Experimental measurements show a monotonic increase in p as a function of the number of fatigue cycles that closely approaches the predicted increase. The experiments also suggest that the relevant dislocation substructures are localized in the material.
Cantrell, John H.↗
Characterization of Nonlinear Rate Dependent Response of Shape Memory Polymers
Shape Memory Polymers (SMPs) are a class of polymers, which can undergo deformation in a flexible state at elevated temperatures, and when cooled below the glass transition temperature, while retaining their deformed shape, will enter and remain in a rigid state. Upon heating above the glass transition temperature, the shape memory polymer will return to its original, unaltered shape. SMPs have been reported to recover strains of over 400%. It is important to understand the stress and strain recovery behavior of SMPs to better develop constitutive models which predict material behavior. Initial modeling efforts did not account for large deformations beyond 25% strain. However, a model under current development is capable of describing large deformations of the material. This model considers the coexisting active (rubber) and frozen (glass) phases of the polymer, as well as the transitions between the material phases. The constitutive equations at the continuum level are established with internal state variables to describe the microstructural changes associated with the phase transitions. For small deformations, the model reduces to a linear model that agrees with those reported in the literature. Thermomechanical characterization is necessary for the development, calibration, and validation of a constitutive model. The experimental data reported in this paper will assist in model development by providing a better understanding of the stress and strain recovery behavior of the material. This paper presents the testing techniques used to characterize the thermomechanical material properties of a shape memory polymer (SMP) and also presents the resulting data. An innovative visual-photographic apparatus, known as a Vision Image Correlation (VIC) system was used to measure the strain. The details of this technique will also be presented in this paper. A series of tensile tests were performed on specimens such that strain levels of 10, 25, 50, and 100% were applied to the material while it was above its glass transition temperature. After deforming the material to a specified applied strain, the material was then cooled to below the glass transition temperature (Tg) while retaining the deformed shape. Finally, the specimen was heated again to above the transition temperature, and the resulting shape recovery profile was measured. Results show that strain recovery occurs at a nonlinear rate with respect to time. Results also indicate that the ratio of recoverable strain/applied strain increases as the applied strain increases.
Volk, Brent↗
Nonlinear viscoelastic characterization of structural adhesives
Measurements of the nonliner viscoelastic behavior of two adhesives, FM-73 and FM-300, are presented and discussed. Analytical methods to quantify the measurements are given and fitted into a framework of an accelerated testing and analysis procedure. The single integral model used is shown to function well and is analogous to a time-temperature stress-superposition procedure (TTSSP). Advantages and disadvantages of the creep power law method used in this study are given.
Rochefort, M. A.↗
Experimental characterization of nonlinear, rate-dependent behavior in advanced polymer matrix composites
In order to support materials selection for the next-generation supersonic civilian-passenger transport aircraft, a study has been undertaken to evaluate the material stress/strain relationships needed to describe advanced polymer matrix composites under conditions of high load and elevated temperature. As part of this effort, this paper describes the materials testing which was performed to investigate the viscoplastic behavior of graphite/thermoplastic and graphite/bismaleimide composites. Test procedures, results and data-reduction schemes which were developed for generating material constants for tension and compression loading, over a range of useful temperatures, are explained.
Gates, Thomas S.↗
Micromechanical characterization of nonlinear behavior of advanced polymer matrix composites
Due to the presence of curing stresses and oriented crystalline structures in the matrix of polymer matrix fiber composites, the in situ nonlinear properties of the matrix are expected to be rather different from those of the bulk resin. A plane stress micromechanical model was developed to retrieve the in situ elastic-plastic properties of Narmco 5260 and Amoco 8320 matrices from measured elastic-plastic properties of IM7/5260 and IM7/8320 advance composites. In the micromechanical model, the fiber was assumed to be orthotropically elastic and the matrix to be orthotropic in elastic and plastic properties. The results indicate that both in situ elastic and plastic properties of the matrices are orthotropic.
Gates, Thomas S.↗
How to characterize the nonlinear amplifier?
The conception of the amplification of the coherent field is formulated. The definition of the coefficient of the amplification as the relation between the mean value of the field at the output to the value at the input and the definition of the noise as the difference between the number of photons in the output mode and square of the modulus of the mean value of the output amplitude are considered. Using a simple example it is shown that by these definitions the noise of the nonlinear amplifier may be less than the noise of the ideal linear amplifier of the same amplification coefficient. Proposals to search another definition of basic parameters of the nonlinear amplifiers are discussed. This definition should enable us to formulate the universal fundamental lower limit of the noise which should be valid for linear quantum amplifiers as for nonlinear ones.
Kallistratova, Dmitri Kouznetsov↗
Experimental characterization of nonlinear processes of whistler branch waves
Explore the source record for details and available documents.
E. M. Tejero↗
Superposition in a class of nonlinear systems
Characterization of nonlinear systems based on linear algebra
NONLINEAR SYSTEM↗
Dimensional analysis of acoustically propagated signals
Traditionally, long term measurements of atmospherically propagated sound signals have consisted of time series of multiminute averages. Only recently have continuous measurements with temporal resolution corresponding to turbulent time scales been available. With modern digital data acquisition systems we now have the capability to simultaneously record both acoustical and meteorological parameters with sufficient temporal resolution to allow us to examine in detail relationships between fluctuating sound and the meteorological variables, particularly wind and temperature, which locally determine the acoustic refractive index. The atmospheric acoustic propagation medium can be treated as a nonlinear dynamical system, a kind of signal processor whose innards depend on thermodynamic and turbulent processes in the atmosphere. The atmosphere is an inherently nonlinear dynamical system. In fact one simple model of atmospheric convection, the Lorenz system, may well be the most widely studied of all dynamical systems. In this paper we report some results of our having applied methods used to characterize nonlinear dynamical systems to study the characteristics of acoustical signals propagated through the atmosphere. For example, we investigate whether or not it is possible to parameterize signal fluctuations in terms of fractal dimensions. For time series one such parameter is the limit capacity dimension. Nicolis and Nicolis were among the first to use the kind of methods we have to study the properties of low dimension global attractors.
Hansen, Scott D.↗
The impact of pulsed RFI on the coded BER performance of the nonlinear satellite communication channel
An examination is conducted of the coded bit error rate (BER) performance of a satellite communication system in which binary phase-shift-keyed (BPSK) modulation is employed, pulsed CW or pulsed noise RFI is present, and the transponder contains a nonlinearity characterized by arbitrary AM/AM and AM/PM characteristics; the RFI pulse duration is further assumed to exceed that of the information symbol. Computed performance curves consider several hypothetical RFI scenarios in which either a hard limiter or an 8 dB clipper represent the transponder amplitude nonlinearity. Results demonstrate the potential seriousness of RFI duty cycles as low as 2 percent, and the fact that CW represents the most severe form of interference.
Weinberg, A.↗
The impact of pulsed RFI on the coded BER performance of the nonlinear satellite communication channel
Communication links from low orbiting spacecraft to a central ground station, via satellite repeater, may be susceptible to significant performance degradation if high-level, pulsed radio frequency interference (RFI) must be contended with. The present paper examines the coded bit error rate (BER) performance of a communication system in which BPSK modulation is employed, pulsed CW or pulsed noise RFI is present, and the transponder contains a nonlinearity characterized by arbitrary AM/AM and AM/PM characteristics. A major result of this paper is an analytic method for determining soft decision statistics of the receiver demodulator output, in which pulsed RFI effects are accounted for. It is demonstrated that this result can be analytically applied to the approximate determination of the BER at the output of a Viterbi decoder, when convolutional coding is employed.
Weinberg, A.↗
Materials and characterization using acoustic nonlinearity parameters and harmonic generation - Effects of crystalline and amorphous structures
The effects of material structure on the nonlinearity parameters are reviewed. Problems discussed include definition of nonlinearity parameters, square-law nonlinearity and collinear beam-mixing, structure dependence of the nonlinearity parameters, negative nonlinearity parameters, and implications for materials characterization.
Cantrell, John H.↗
An Experimental Investigation on the Static Equilibria and Dynamics of Liquid Bridges
A liquid bridge is a volume of liquid held between two or more solid supports. In the case of small disk supports with a sharp edge, the contact line between the bridge and the support disk will be anchored along the edge of the disk. For these cases the solid presents a geometrical singularity and the contact angle is indeterminate within a given range. This dissertation presents research conducted on liquid bridges with anchored contact lines. The three major topics covered are: determining the role of support geometry on static equilibria, liquid bridge dynamical behavior, and forces exerted by a liquid bridge on a support structure. The work was primarily experimental and conducted in a "Plateau tank" that allowed for the simulation of equivalent low-gravity conditions. The main thrust of the experimental work involved the use of a high resolution optical measurement system for imaging the dynamic zone shape, measurement of the static and dynamic contact angles and non-invasive analysis of excited surface modes. The liquid bridge was manipulated by computer controlled linear actuators which allowed precise control over the physical characteristics of the bridge. Experiments have been carried out to locate a bifurcation point along the maximum volume axisymmetric stability margin. Below the critical slenderness the bifurcation from an axisymmetric to a stable nonaxisymmetric configuration is supercritical. However, above this critical slenderness, the bifurcation is subcritical. A series of experiments analyzed the effect on axisymmetric bridge stability by using support disks of different radii, The shape behavior as transition points were approached, as well as the limiting case of a vanishing support radius was investigated. Experiments were performed to determine the resonant frequencies of axisymmetric bridges subject to lateral vibrations. Anomolous results led to a series of experiments to characterize nonlinearities present in the dynamic bridge shape. Finally, an attempt was made to experimentally measure the force exerted by the bridge on the lower support disk. This was done through use of a force balance apparatus. Particular attention was paid to the behavior of the bridge as the minimum volume stability limit was approached.
Resnick, Andrew Howard↗