Material damping - An introductory review of mathematical models, measures and experimental techniques.
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Bert, C. W.↗
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A mathematical model for storied buildings subjected to automatic loom stresses
Expressions are derived for the displacements of a many storied building subjected to the action of classical weaving looms located at different levels of the building. The building is regarded as a vertical fixed beam with a uniformly distributed mass as well as concentrated masses at each level. The calculation relations are obtained on the assumption of harmonic variation of the forces acting at each level as well as the assumption of narrow band stationary random excitatory forces.
Stan, A.↗
Use of the mathematical modelling method for the investigation of dynamic characteristics of acoustical measuring instruments
The schematic diagram of a noise measuring device is presented that uses pulse expansion modeling according to the peak or any other measured values, to obtain instrument readings at a very low noise error.
Vasilyev, Y. M.↗
A mathematical modeling method for determination of local vibroacoustic characteristics of structures
A method is proposed for determining vibroacoustic characteristics from the results of measurements of the distribution of vibrational energy in a structure. The method is based on an energy model of a structure studied earlier. Equations are written to describe the distribution of vibrational energy in a hypothetical diffuse energy state in structural elements.
Tartakovskiy, B. D.↗
Mathematical models for the reflection coefficients of dielectric half-spaces
The reflection coefficients at normal incidence are found for a large class of one-dimensionally inhomogeneous or stratified half-spaces, which contain a homogeneous half-space. The formulation of the problem involves a combination of the classical boundary value technique, and the nonclassical principle of invariant imbedding. Solutions are in closed form and expressible in terms of Bessel functions. All results are given in terms of the ratio of the distance between free space and the homogeneous half-space to the wavelength in vacuo. One special case is that of an arbitrary number of layers lying on a homogeneous half-space where the dielectric constant of each layer has a constant gradient. A number of other special cases, limiting cases, and generalizations are developed including one in which the thickness of the top layer obeys a probability distribution.
Evans, D. D.↗
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.↗
Toward a mathematical model of solar radiation for engineering analysis of solar energy systems
The currently most-used insolation model and what improvements might be made in it to better suit it for use in designing energy systems is discussed. An approach to constructing an upgraded model is sketched.
Hamilton, C. L.↗
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.↗
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.↗
Mathematical modeling of waste heat management alternatives for the United States
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Plass, H. J., Jr.↗
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.
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Application of LANDSAT satellite imagery and oceanographic data for verification of an upwelling mathematical model
The author has identified the following significant results. Data obtained during the cruise of the Cabo Frio and from LANDSAT imagery are used to discuss the characteristics of a linear model which simulates wind induced currents calculated from meteorological conditions at the time of the mission. There is a significant correspondance between the model of simulated horizontal water circulation, sea surface temperature, and surface currents observed on LANDSAT imagery. Close approximations were also observed between the simulation of vertical water movement (upwelling) and the oceanographic measurements taken along a series of points of the prevailing currents.
Dejesusparada, N.↗
Mathematical model investigation of long-term transport of ocean-dumped sewage sludge related to remote sensing
An existing, three-dimensional, Eulerian-Lagrangian finite-difference model was modified and used to examine the transport processes of dumped sewage sludge in the New York Bight. Both in situ and laboratory data were utilized in an attempt to approximate model inputs such as mean current speed, horizontal diffusion coefficients, particle size distributions, and specific gravities. The results presented are a quantitative description of the fate of a negatively buoyant sewage sludge plume resulting from continuous and instantaneous barge releases. Concentrations of the sludge near the surface were compared qualitatively with those remotely sensed. Laboratory study was performed to investigate the behavior of sewage sludge dumping in various ambient density conditions.
Kuo, C. Y.↗
Frost formation on an airfoil: A mathematical model 1
A computer model to predict the frost formation process on a flat plate was developed for application to most environmental conditions under which frost occurs. The model was analytically based on a generalized frost thermal conductivity expression, on frost density and thickness rate equations, and on modified heat and mass transfer coefficients designed to fit the available experimental data. The broad experimental ranges reflected by the extremes in ambient humidities, wall temperatures, and convective flow properties in the various publications which were examined served to severely test the flexibility of the model. An efficient numerical integration scheme was developed to solve for the frost surface temperature, density, and thickness under the changing environmental conditions. The comparison of results with experimental data was very encouraging.
Dietenberger, M.↗
Mathematical model for preventive maintenance scheduling
A model is formulated to describe the effect of the time interval chosen for preventive maintenance upon the frequency of failure and frequency of total maintenance. Trade-offs between these two frequencies are determined by computation of an optimal interval in the case where the failure distribution is known. For unknown distributions, an adaptive statistical technique is developed that converges to an optimal preventive maintenance interval. A numerical illustration is given.
Lorden, G.↗
The Application of Systems Analysis and Mathematical Models to the Study of Erythropoiesis During Space Flight
Included in the report are: (1) review of the erythropoietic mechanisms; (2) an evaluation of existing models for the control of erythropoiesis; (3) a computer simulation of the model's response to hypoxia; (4) an hypothesis to explain observed decreases in red blood cell mass during weightlessness; (5) suggestions for further research; and (6) an assessment of the role that systems analysis can play in the Skylab hematological program.
Leonard, J. I.↗