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Results for “PRONY SERIES”

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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13 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Determining a Prony Series for a Viscoelastic Material From Time Varying Strain Data

In this study a method of determining the coefficients in a Prony series representation of a viscoelastic modulus from rate dependent data is presented. Load versus time test data for a sequence of different rate loading segments is least-squares fitted to a Prony series hereditary integral model of the material tested. A nonlinear least squares regression algorithm is employed. The measured data includes ramp loading, relaxation, and unloading stress-strain data. The resulting Prony series which captures strain rate loading and unloading effects, produces an excellent fit to the complex loading sequence.

Tzikang, Chen↗
NASA NTRS1995

Fitting Prony Series To Data On Viscoelastic Materials

Improved method of fitting Prony series to data on viscoelastic materials involves use of least-squares optimization techniques. Based on optimization techniques yields closer correlation with data than traditional method. Involves no assumptions regarding the gamma'(sub i)s and higher-order terms, and provides for as many Prony terms as needed to represent higher-order subtleties in data. Curve-fitting problem treated as design-optimization problem and solved by use of partially-constrained-optimization techniques.

Hill, S. A.↗
NASA NTRS1988

Numerical solution methods for viscoelastic orthotropic materials

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Gramoll, K. C.↗
NASA NTRS1993

The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Hill, S. A.↗
NASA NTRS1997

Quasi-Static Viscoelasticity Loading Measurements of an Aircraft Tire

Stair-step loading, cyclic loading, and long-term relaxation tests were performed on an aircraft tire to observe the quasi-static viscoelastic response of the tire. The data indicate that the tire continues to respond viscoelastically even after it has been softened by deformation. Load relaxation data from the stair-step test at the 15,000-lb loading was fit to a monotonically decreasing Prony series.

Mason, Angela J.↗
NASA NTRS2003

An Approximate Dissipation Function for Large Strain Rubber Thermo-Mechanical Analyses

Mechanically induced viscoelastic dissipation is difficult to compute. When the constitutive model is defined by history integrals, the formula for dissipation is a double convolution integral. Since double convolution integrals are difficult to approximate, coupled thermo-mechanical analyses of highly viscous rubber-like materials cannot be made with most commercial finite element software. In this study, we present a method to approximate the dissipation for history integral constitutive models that represent Maxwell-like materials without approximating the double convolution integral. The method requires that the total stress can be separated into elastic and viscous components, and that the relaxation form of the constitutive law is defined with a Prony series. Numerical data is provided to demonstrate the limitations of this approximate method for determining dissipation. Rubber cylinders with imbedded steel disks and with an imbedded steel ball are dynamically loaded, and the nonuniform heating within the cylinders is computed.

Johnson, Arthur R.↗
NASA NTRS2019

Micromechanical Modeling of High-Strain Thin-Ply Composites

This paper presents a micromechanical analysis for the elastic and viscoelastic behavior of high-strain thin-ply composites. The modeling approach is based on unit cell homogenization. The geometry of the internal weave architecture and ply configuration is characterized via micrographic analysis and explicitly modeled in the unit cell. The composites are modeled as Kirchhoff plates and the homogenization analysis computes the effective relaxation ABD matrix represented by Prony series using the elastic and viscoelastic properties of the constituent fiber and matrix. The formulation of the micromechanical model and numerical implementation d. Composite laminates with 3-ply and 4-ply configurations are studied.

Hamillage, Milinda Yapa↗
NASA NTRS1986

Application of physical parameter identification to finite element models

A time domain technique for matching response predictions of a structural dynamic model to test measurements is developed. Significance is attached to prior estimates of physical model parameters and to experimental data. The Bayesian estimation procedure allows confidence levels in predicted physical and modal parameters to be obtained. Structural optimization procedures are employed to minimize an error functional with physical model parameters describing the finite element model as design variables. The number of complete FEM analyses are reduced using approximation concepts, including the recently developed convoluted Taylor series approach. The error function is represented in closed form by converting free decay test data to a time series model using Prony' method. The technique is demonstrated on simulated response of a simple truss structure.

Bronowicki, Allen J.↗
NASA NTRS1991

Determination of a natural basis function set on thick, structured slabs using Prony's method

The calculation of currents on a thick, structured slab such as a thick slab of honeycomb is discussed. Unfortunately, for certain applications, the slab can be on the order of several wavelengths, so that the straightforward application of the method of moments using subdomain basis functions is too expensive. The authors discuss how to apply Prony's method to the currents calculated for a thin, structured slab to obtain a natural set of basis functions to represent the currents in the interior of a thick slab. Prony's method represents the currents as a series of complex exponential functions. The thick slab problem is then solved by the method of moments using subdomain basis functions near the slab interfaces and one or two of the complex exponentials as basis functions within the slab.

Jorgenson, Roy E.↗
NASA NTRS1984

On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.

Chao, B. F.↗
NASA NTRS1973

The effects of changes in response-independent pay upon human masseter EMG

Electromyographic activity of the masseter muscle was recorded in five human subjects who were presented with systematically varied rates of non-contingent pay. Rates of pay were varied between sessions in either a descending or an ascending series. The number of masseter contractions was found to be greater during the descending series than during the ascending series, especially when a descending series of pay changes followed an ascending series. Verbal physical displays of anger and aggression were noted during descending series. These data indicated a possible relation between masseter contractions and aggression.

Proni, T. J.↗
NASA NTRS1991

Signal processing techniques for clutter filtering and wind shear detection

An extended Prony algorithm applicable to signal processing techniques for clutter filtering and windshear detection is discussed. The algorithm is based upon modelling the radar return as a time series, and appears to offer potential for improving hazard factor estimates in the presence of strong clutter returns.

Baxa, Ernest G., Jr.↗