Second-order planetary theory. Part 1 - Outline of the method
Brouwers theory of planetary motion for second- order perturbation computation using Fourier series
Hamid, S. E.↗
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Radiation and near-field coupling between two collinear open-ended waveguides.
Radiating collinear open ended waveguides and near field coupling analyzed using simultaneous integral equations and Fourier series expansion of aperture field
Mailloux, R. J.↗
The time-varying elastic properties of the left ventricular muscle
Left ventricular muscle time varying elastic properties, using dynamic model and Fourier series representations
Ghista, D. N.↗
Calculations of ion-cyclotron wave properties in hot plasmas
Fields and power transfer for electromagnetic waves in hot plasma calculated using Fourier integral and Fourier series methods
Sigman, D. R.↗
High efficiency telemetry method
Analog and digital mechanizations contain new combinations of known circuits that generate coefficients of Fourier series terms in accordance with harmonic content of waveform to be transmitted. Technique represents information signal more accurately that previous methods and requires fewer information bits.
Lim, L. Y.↗
Theoretical pressure distributions over arbitrarily shaped periodic waves in subsonic compressible flow and comparison with experiment
Theoretical solution for pressure distribution over arbitrarily shaped periodic waves using Fourier series
Czarnecki, K. R.↗
Calculation of linearized supersonic flow over slender cones of arbitrary cross section
Supersonic linearized conical-flow theory is used to determine the flow over slender pointed cones having horizontal and vertical planes of symmetry. The geometry of the cone cross sections and surface velocities are expanded in Fourier series. The symmetry condition permits the uncoupling of lifting and nonlifting solutions. The present method reduces to Ward's theory for flow over a cone of elliptic cross section. Results are also presented for other shapes. Results by this method diverge for cross-sectional shapes where the maximum thickness is large compared with the minimum thickness. However, even for these slender-body shapes, lower order solutions are good approximations to the complete solution.
Mascitti, V. R.↗
Magnetohydrodynamic generator experimental studies
The results for an experimental study of a one wavelength MHD induction generator operating on a liquid flow are presented. First the design philosophy and the experimental generator design are summarized, including a description of the flow loop and instrumentation. Next a Fourier series method of treating the fact that the magnetic flux density produced by the stator is not a pure traveling sinusoid is described and some results summarized. This approach appears to be of interest after revisions are made, but the initial results are not accurate. Finally, some of the experimental data is summarized for various methods of excitation.
Pierson, E. S.↗
Theoretical study of stress concentrations at circular holes and inclusions in strain hardening materials.
Nonlinear boundary value problems of an infinite elastic-plastic plate with a circular hole subjected to pure tension and pure shear at infinity are solved by a method involving Fourier series and finite difference. On the basis of these solutions, the validity of Neuber's relationship between the stress and strain concentration factors for the plane stress problems is examined and a generalized Stowell formula for the stress concentration factor is proposed for problems in which the applied loading may be pure shear as well as pure tension and, furthermore, other stress states. By the same method of solution, the stress distributions around a rigid circular cylindrical inclusion embedded in an infinite rigid-plastic matrix subjected to uniform transverse pure shear and tension are obtained.
Huang, W. C.↗
Closed form solution to the semi-infinite cylindrical shell problem.
Reconsideration of the problem of a complete semiinfinite circular cylindrical shell with a square cage investigated earlier by Reissner and Simmonds (1966). It is shown that the solution can be found in closed form rather than in the form of Fourier series, provided that the boundary data on the end of the shell are 'slowly varying.'
Sanders, J. L., Jr.↗
A semi-analytical method of computation of oceanic tidal perturbations in the motion of artificial satellites
The method of expansion of the satellite's perturbations, as caused by the oceanic tides, into Fourier series is discussed. The coefficients of the expansion are purely numerical and peculiar to each particular satellite. Such a method is termed as semi-analytical in celestial mechanics. Gaussian form of the differential equations for variation of elements, with the right hand sides averaged over the orbit of the satellite, is convenient to use with the semi-analytical expansion.
Musen, P.↗
Numerical analysis of stiffened shells of revolution. Volume 7: Satellite programs for the STARS system
The user and programming information necessary for the application of the SATELLITE programs for the STARS system are presented. The individual program functions are: (1) data debugging for the STARS-2S program, (2) Fourier series conversion program, (3) data debugging for the STARS-2B program, and (4) data debugging for the STARS-2V program.
Svalbonas, V.↗
Comparison of finite-difference schemes for analysis of shells of revolution
Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.
Noor, A. K.↗
Experimental and data analysis techniques for deducing collision-induced forces from photographic histories of engine rotor fragment impact/interaction with a containment ring
An analysis method termed TEJ-JET is described whereby measured transient elastic and inelastic deformations of an engine-rotor fragment-impacted structural ring are analyzed to deduce the transient external forces experienced by that ring as a result of fragment impact and interaction with the ring. Although the theoretical feasibility of the TEJ-JET concept was established, its practical feasibility when utilizing experimental measurements of limited precision and accuracy remains to be established. The experimental equipment and the techniques (high-speed motion photography) employed to measure the transient deformations of fragment-impacted rings are described. Sources of error and data uncertainties are identified. Techniques employed to reduce data reading uncertainties and to correct the data for optical-distortion effects are discussed. These procedures, including spatial smoothing of the deformed ring shape by Fourier series and timewise smoothing by Gram polynomials, are applied illustratively to recent measurements involving the impact of a single T58 turbine rotor blade against an aluminum containment ring. Plausible predictions of the fragment-ring impact/interaction forces are obtained by one branch of this TEJ-JET method; however, a second branch of this method, which provides an independent estimate of these forces, remains to be evaluated.
Yeghiayan, R. P.↗
Theory of a ring laser
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Menegozzi, L. N.↗
Development of programs for computing characteristics of ultraviolet radiation
Efficient programs were developed for computing all four characteristics of the radiation scattered by a plane-parallel, turbid, terrestrial atmospheric model. They were developed (FORTRAN 4) and tested on the IBM /360 computers with 2314 direct access storage facility. The storage requirement varies between 200K and 750K bytes depending upon the task. The scattering phase matrix (or function) is expanded in a Fourier series whose number of terms depend upon the zenith angles of the incident and scattered radiations, as well as on the nature of aerosols. A Gauss-Seidel procedure is used for obtaining the numerical solution of the transfer equation.
Dave, J. V.↗
Computations of M sub 2 and K sub 1 ocean tidal perturbations in satellite elements
Semi-analytic perturbation equations for the influence of M2 and K1 ocean tidal constituents on satellite motion are expanded into multi-dimensional Fourier series and calculations made for the BE-C satellite. Perturbation in the orbital elements are compared to those of the long period solid earth tides.
Estes, R. H.↗
Analysis of three-component aeromagnetic data
The numerical method of obtaining three field components from total field measurements, using double Fourier series expansion, is presented. The expressions for moments of the anomalous field components over a finite area are given. The magnitude and direction of the magnetization vector indicate that the vertical component of the magnetic field calculated from total field observations is more accurate at higher geomagnetic latitudes than at lower latitudes. The opposite is true for the horizontal components. The error in determining the magnetization vector directions are significantly large over most of the range of variation of declination and inclination of the vector, demonstrating the practical limitations of computing field components from total field data even under the best of conditions.
Bhattacharyya, B. K.↗