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At least 163 records · Page 9

SINDA - Systems Improved Numerical Differencing Analyzer

Capability to model fluid flow added. SINDA is software system developed to solve physical problems governed by diffusion-type equations mathematically modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations. Adapted to wide range of problems represented by Fourier, Possion, Laplace, or other differential equations. Written in FORTRAN and Assembler.

Damico, Steve J.↗

Dynamic response of a semi-infinite elastic cylinder containing an acoustic medium.

The solutions developed in this paper are based on the finite Hankel-Fourier-Laplace transform. The Love-Timoshenko shell equations are reduced through the application of the Fourier-Laplace transforms to the axial space and time variables. The equation of motion for the acoustic fluid contained within the shell are reduced through the application of the finite Hankel-Fourier-Laplace transform to the radial, axial spatial, and time variables. The boundary conditions at the fixed end of the semi-infinite shell are met through the application of loadings symmetric with respect to the origin and the application of a ring loading at the origin which is chosen so as to make the radial deflection there zero. Expressions are found for the transforms of the axial, tangential, and radial shell displacements, the axial, tangential, and radial fluid velocities, and the radiated fluid pressure. Numerical inversion of the Fourier-Laplace transform is accomplished in terms of a series of ultraspherical polynomials and Gauss-Hermite or Gauss-Laguerre quadrature.

Carpenter, R. F., III↗

SINDA '85/FLUINT, Version 2.2

SINDA, Systems Improved Numerical Differencing Analyzer, software system developed for solving physical problems governed by diffusion-type equations modeled by lumped-parameter representations. Used as general thermal analyzer with resistor-and-capacitor-network representations, adapted to wide range of problems represented by such differential equations as Fourier, Poisson, or LaPlace. Software system updated. FLUINT, FLUid INTegrator, is advanced, one-dimensional fluid-analysis program solving equations of arbitrary fluid-flow networks. Written in FORTRAN and ASSEMBLER.

Cullimore, Brent↗

I-BIEM, an iterative boundary integral equation method for computer solutions of current distribution problems with complex boundaries: A new algorithm. I - Theoretical

A new algorithm for an iterative computation of solutions of Laplace's or Poisson's equations in two dimensions, using Green's second identity, is presented. This algorithm converges strongly and geometrically and can be applied to curved, irregular, or moving boundaries with nonlinear and/or discontinuous boundary conditions. It has been implemented in Pascal on a number of micro- and minicomputers and applied to several geometries. Cases with known analytic solutions have been tested. Convergence to within 0.1 percent to 0.01 percent of the theoretical values are obtained in a few minutes on a microcomputer.

Cahan, B. D.↗

Heat transfer characteristics of an emergent strand

A mathematical model was developed to describe the heat transfer characteristics of a hot strand emerging into a surrounding coolant. A stable strand of constant efflux velocity is analyzed, with a constant (average) heat transfer coefficient on the sides and leading surface of the strand. After developing a suitable governing equation to provide an adequate description of the physical system, the dimensionless governing equation is solved with Laplace transform methods. The solution yields the temperature within the strand as a function of axial distance and time. Generalized results for a wide range of parameters are presented, and the relationship of the results and experimental observations is discussed.

Simon, W. E.↗

Coupling finite and boundary element methods for two-dimensional potential problems

A finite element-boundary element (FE-BE) coupling method based on a weighted residual variational method is presented for potential problems, governed by either the Laplace or the Poisson equations. In this method, a portion of the domain of interest is modeled by finite elements (FE) and the remainder of the region by boundary elements (BE). Because the BE fundamental solutions are valid for infinite domains, a procedure that limits the effects of the BE fundamental solution to a small region adjacent to the FE region, called the transition region (TR), is developed. This procedure involves a judicious choice of functions called the transition (T) functions that have unit values on the BE-TR interface and zero values on the FE-TR interface. The present FE-BE coupling algorithm is shown to be independent of the extent of the transition region and the choice of the transition functions. Therefore, transition regions that extend to only one layer of elements between FE and BE regions and the use of simple linear transition functions work well.

Krishnamurthy, T.↗

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

Lemoine, Frank↗

Tidal Friction in the Earth-Moon System and Laplace Planes: Darwin Redux

The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than ∼10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.

Darwin Redux↗

ISAC - A tool for aeroservoelastic modeling and analysis

This paper discusses the capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrate some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

ISAC: A tool for aeroservoelastic modeling and analysis

The capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules is discussed. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrates some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

Transfer Functions Via Laplace- And Fourier-Borel Transforms

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

Can, Sumer↗

Electromagnetic plasma wave propagation along a magnetic field

The linearized response of a Vlasov plasma to the steady-state excitation of transverse plasma waves along an external magnetic field is examined. Assuming a delta-function excitation mechanism, and performing a detailed Vlasov-Maxwell equation analysis using Fourier-Laplace transforms, the plasma response is found to consist of three terms: a branch-cut term, a free-streaming term, and a dielectric-pole term. Also considered is the phenomenon of plasma wave echoes. The case of longitudinal electrostatic waves is extended to the case of transverse plasma waves that propagate along an external magnetic field. It is shown that a transverse echo results in lowest order only when one excitation is transverse and the other is longitudinal.

Olson, C. L.↗

Design for active flutter suppression and gust alleviation using state-space aeroelastic modeling

An analytical design technique for an active flutter-suppression and gust-alleviation control system is presented. It is based on a rational approximation of the unsteady aerodynamic loads in the entire Laplace domain, which yields matrix equations of motion with constant coefficients. Some existing rational approximation schemes are reviewed, and a new technique which yields a minimal number of augmented states for a desired accuracy is presented. The state-space aeroelastic model is used to design a constant gain, partial-feedback control system, which simultaneously assures stability and optimizes any desired combination of gust response parameters throughout the entire flight envelope.

Karpel, M.↗

Design for active and passive flutter suppression and gust alleviation

Analytical design techniques for active and passive control of aeroelastic systems are based on a rational approximation of the unsteady aerodynamic loads in the entire Laplace domain, which yields matrix equations of motion with constant coefficients. Some existing schemes are reviewed, the matrix Pade approximant is modified, and a technique which yields a minimal number of augmented states for a desired accuracy is presented. The state-space aeroelastic model is used to design an active control system for simultaneous flutter suppression and gust alleviation. The design target is for a continuous controller which transfers some measurements taken on the vehicle to a control command applied to a control surface. Structural modifications are formulated in a way which enables the treatment of passive flutter suppression system with the same procedures by which active control systems are designed.

Karpel, M.↗

Time-dependent shock acceleration of energetic electrons including synchrotron losses

The present investigation of the time-dependent particle acceleration problem in strong shocks, including synchrotron radiation losses, solves the transport equation analytically by means of Laplace transforms. The particle distribution thus obtained is then transformed numerically into real space for the cases of continuous and impulsive injections of particles at the shock. While in the continuous case the steady-state spectrum undergoes evolution, impulsive injection is noted to yield such unpredicted features as a pile-up of high-energy particles or a steep power-law with time-dependent spectral index. The time-dependent calculations reveal varying spectral shapes and more complex features for the higher energies which may be useful in the interpretation of outburst spectra.

Fritz, Klaus-Dieter↗