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At least 721 records · Page 40

QUICK-GEOMETRY, a rapid response method for mathematically modeling configuration geometry

The philosophy, development, and various applications of the QUICK-GEOMETRY system were outlined. This system provides a practical method for developing the geometry models that are essential to the operation of computer-based design and manufacturing systems. Of particular interest are the various methods for modeling surface geometry that are used by aerodynamic analysis codes.

Vachris, A. F., Jr.↗

Mathematical formulation for the propagation of sound through a turbulent jet

The sound propagation through a nonuniform turbulent jet flow field is studied by means of a system of linearized equations governing the acoustic variables. These equations depend on the fluctuating flow-field variables which can be prescribed by experimental results. It is shown that the correlations of the acoustic variables depend throughout the flow field on the space-time correlation of the turbulent velocities and on the mean flow variables and their gradients.

Gunzburger, M.↗

Mathematical model of fires

Model allows predictions of future development of fire and can be used to evaluate different control methods at particular stages of fire. Five constraints considered are flame-spread rate, fuel-surface limit, airflow limit, quantity of fuel, original quantity of air.

Coulbert, C. D.↗

Mathematical modelling of undrained clay behavior

The proposed general analytical model describes the anisotropic, elastoplastic, path-dependent, stress-strain properties of inviscid saturated clays under undrained conditions. Model parameters are determined by using results from strain-controlled simple shear tests on a saturated clay. The model's accuracy is evaluated by applying it to predict the results of other tests on the same clay, including monotonic and cyclic loading. The model explains the very anisotropic shear strength behavior observed for weak marine clays.

Prevost, J. H.↗

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Bielawa, R. L.↗

A mathematical force and moment model of a UH-1H helicopter for flight dynamics simulations

A model of a UH-1H helicopter was developed to support flight simulations and for developmental work on an avionics system known as V/STOLAND system. Equations and numerical values of constants used to represent the helicopter are presented. Responses to stop inputs of the cyclic and collective controls are shown and compared with flight test data for a UH-1H. The model coefficients were adjusted in an attempt to get a consistant match with the flight time histories at hover and 60 knots. Response matching was obtained at 60 knots, but the matching at hover was not as successful. Pilot evaluations of the model, both fixed and moving base, were made.

Talbot, P. D.↗

Some basic mathematical methods of diffusion theory

An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.

Giere, A. C.↗

On the mathematical conditions for the existence of periodic fluctuations in non-uniform media

The assumption that periodic excitations result in periodic responses for the case of waves propagating through nonuniform media is examined by investigating the periodic solutions of linear hyperbolic differential equations whose coefficients vary with position and whose solution must satisfy periodic boundary or source data. It is shown that the nature of the coefficients of undifferentiated terms of the differential system is crucial in determining whether the solution is periodic. Particular attention is paid to the propagation of infinitesimal pressure waves through the nonuniform steady flow of a lossless fluid.

Gunzburger, M. D.↗

A mathematical analysis of the theory of interplanetary scintillation in the weak scattering approximation

A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.

Mitchell, D. G.↗

Mathematical models for the reflection coefficients of lossy dielectric half-spaces with application to transient responses of chirped pulses

Reflection coefficients are found at normal incidence for a large class of homogeneous lossy half-spaces with a one-dimensionally inhomogeneous or stratified lossy layer on top. Solutions are in terms of Hankel functions of complex argument to decrease cancellation error at high frequencies. One special case is that of layers on a homogeneous half-space where the dielectric constant in each layer may vary in a quite general manner. A Wronskian is used to insure the critical computations are correct. The reflection of chirped pulses is considered. Solutions are obtained by applying the fast Fourier transform. It is found that for a typical relatively long normalized 'long' pulse the power reflected as a function of time is essentially the power reflection coefficient for the frequencies swept out, whereas for a relatively short 'long' pulse, with the same relative change in frequency and the same number of oscillations there is only the uniform attenuation by the power reflection coefficient of the center frequency. By a 'long' pulse we mean a pulse whose spatial length is long compared to the thickness of the reflecting layer.

Evans, D. D.↗

Solar polar coronal hole - A mathematical simulation

The northern polar region of the sun was studied during July 1973 by Munro and Jackson through use of the white-light coronagraph and the X-ray photographs produced by the Skylab mission. They described the northern polar hole as nearly axisymmetric and gave the geometry and density distribution under this approximation. The present work gives quasi-radial approximation to the full magnetohydrodynamic equations for axisymmetric, polytropic solar wind flow to simulate this polar hole, with the benefit that model temperature and magnetic field intensities and distributions in this particular polar hole can be deduced. It is concluded that from 2 out to 5 solar radii the temperature varies only slightly with radius, but is larger near the center of the polar hole than at the edge. It is also found that the magnetic field intensity at 2 solar radii could be about 1 gauss at the center of the hole, decreasing toward the edge of the hole. If this is extrapolated to the surface, a field as high as 20 gauss is suggested.

Suess, S. T.↗

Rotor systems research aircraft simulation mathematical model

An analytical model developed for evaluating and verifying advanced rotor concepts is discussed. The model was used during in both open loop and real time man-in-the-loop simulation during the rotor systems research aircraft design. Future applications include: pilot training, preflight of test programs, and the evaluation of promising concepts before their implementation on the flight vehicle.

Houck, J. A.↗

Mathematical modelling of a human external respiratory system

A closed system of algebraic and common differential equations solved by computer is investigated. It includes equations which describe the activity pattern of the respiratory center, the phrenic nerve, the thrust produced by the diaphragm as a function of the lung volume and discharge frequency of the phrenic nerve, as well as certain relations of the lung stretch receptors and chemoreceptors on various lung and blood characteristics, equations for lung biomechanics, pulmonary blood flow, alveolar gas exchange and capillary blood composition equations to determine various air and blood flow and gas exchange parameters, and various gas mixing and arterial and venous blood composition equations, to determine other blood, air and gas mixing characteristics. Data are presented by means of graphs and tables, and some advantages of this model over others are demonstrated by test results.

Source record↗

Mathematical simulation of power conditioning systems. Volume 1: Simulation of elementary units. Report on simulation methodology

Methods and algorithms used for the simulation of elementary power conditioning units buck, boost, and buck-boost, as well as shunt PWM are described. Definitions are given of similar converters and reduced parameters. The various parts of the simulation to be carried out are dealt with; local stability, corrective network, measurements of input-output impedance and global stability. A simulation example is given.

Prajous, R.↗