Showing papers in "AIAA Journal in 1969"

A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows.

Abstract: Approximate solutions from the linearized formulation are obtained by idealizing the surface as a set of lifting elements which are short line segments of acceleration-potential doub? lets. The normal velocity induced by an element of unit strength is given by an integral of the subsonic kernel function. The load on each element is determined, by, satisfying normal velocity boundary conditions at a set of points oil the surface. It is seen a posteriori

Stability of periodic orbits in the elliptic, restricted three-body problem.

Abstract: A systematic study has been made of periodic orbits in the two-dimensional, elliptic, restricted three-body problem. All ranges of eccentricities, from 0 to 1, and mass-ratios, from 0 to J, have been investigated. Eleven hundred periodic orbits have been obtained. It is concluded that the elliptic problem behaves in a way which is completely different from the circular problem. The main difference is in the stability properties of the periodic orbits. Because of the nonexistence of the Jacobi integral (the elliptic problem is not conservative), the characteristic equation of the monodromy matrix does not have a pair of unit roots, in general. The stability is denned by two real numbers (stability indices) rather than one. Because of that, there are seven general classes of periodic orbits, according to their stability properties. The stability of the periodic orbits has been determined by numerically integrating the variational equations with a recurrent power series method. The results are in contrast with the circular problem, where there are only three classes of orbits (stability, even instability, and odd instability): in the elliptic problem there are one stable class and six unstable classes. The elliptic, restricted three-body problem can be considered as the prototype of all nonintegrable, nonconservative Hamiltonian systems, and in this paper, probably for the first time, a classification of the multipliers is given for these systems. I. Introduction

Basic relations for control of flexible vehicles

Abstract: Papers written on the control of flexible vehicles have primarily concerned themselves with a particular example or a particular class of vehicles. Even in these restricted studies, computer solutions are generally used and little insight is offered into the basic initial approach to designing a "control system/flexible vehicle" combination from scratch. Therefore, in this paper an attempt is made to indicate the basic relationships that enter into the control of flexible vehicles, and to show that these relationships are the same for a variety of flexible vehicle types and are not limited to those displaying only bending modes. Further, for several fundamental cases, simple analytic approximations are presented for the system characteristic roots, which can both guide the system design and provide a measure of the system response. The approach is illustrated by comparing the analytic approximations with computer results for several simple vehicles.

The eigenvalue problem for structural systems with statistical properties.

Abstract: The treatment of matrix eigenvalue problems with statistical properties is presented in a general form including correlation between matrix elements. Linear equations are formulated for the statistics of the eigenvectors as well as eigenvalues. Results are applied to dynamic systems and verified by an independent Monte Carlo simulation. Although the applications in this study are all structural systems, the theory as developed is applicable to any problem leading to similar eigenvalue equations.

Effect of turbulent fluctuations in an optically active fluid medium.

Abstract: The effect of a beam traversing an optically active medium of turbulent fluctuations of the index of refraction in the medium is investigated theoretically. The general far-field case is solved by integration of the wave equation with both gain and fluctuations of the index refraction, simplified by neglecting the Laplacian of the fluctuating part of the electric field and one of the time derivatives. The far-field diffraction pattern is identical to that for a nonactive medium. For small to moderate extinction there is a loss of power from the coherent beam but only a slight change in the diffraction pattern, accompanied by wide-angle incoherent scattering. For high-gain cases it is possible to have the extinction coefficient less than the gain, but with complete extinction of the coherent beam and a large incoherent scattering pattern. The use of a more realistic turbulence spectrum than previously used has led to the discovery of a second branch in the resolution curve, in which the resolution far exceeds the previously given "limiting resolution" as the aperture size is increased beyond a certain limit, and approaches the diffraction pattern based on the aperture, although there may be considerable attenuation in the intensity in the diffraction pattern of the coherent beam. These results are applicable, for example, to the use of large aperture optics in turbulene wind tunnels.

Calculation of Turbulent Boundary Layers on Rough Surfaces in Pressure Gradient

Abstract: Rough surface skin-friction relations previously described in the literature are expanded in scope and range of applicability . The resulting equations are combined with the momemtum integral equation and an auxiliary equation for the shape factor to provide a calculation method for predicting the growth of the turbulent boundary layer over a rough surface in pressure gradient. Several comparisons have been made between the calculation method and available experimental data in zero, favorable, and adverse pressure gradients. The agreement in general is good.

Turbulence Measurements in the Wake of a Thin Flat Plate

Abstract: First the two-dimensionality of the flow was checked by measuring mean velocity and turbulence level profiles at different spanwise positions, and the flow was found uniform over 75% of the span (wind-tunnel width) at the trailing edge and over 60% of the span at the last downstream station, x = 240 cm, where wake measurements were taken. No detectable periodic components were found in the wake at any downstream station as evidenced either by wave analyzer or by correlation measurements taken with two probes located symmetrically to the centerline and placed near the location of maximum shear stress in the wake. The characteristics of the turbulent boundary layer at the trailing edge (x = 0) were the following: conventional thickness (U/Um = 0.99) d = 5.50 cm, momentum thickness d = 0.58 cm, and shape parameter H = 5*/6 = 1.44. At the same location, the friction velocity was found to be u*/Um = 0.046. This value was obtained by using Clauser's logarithmic law.5 The wall slope method using hot-wire measurements with correction for proximity of the boundary due to Wills 4 yielded a value of u*/Ua = 0.037. The thickness of the trailing edge expressed nondimensionally was quite small, u*h/v = 3; in other words, much smaller than the viscous sublayer. All data is presented in dimensionless form using 00, the momentum thickness at the trailing edge and the undisturbed flow velocity Um as reference quantities. Symmetry of the wake was found to be excellent and representative

Vibration analysis by dynamic partitioning.

Abstract: process of iteration, thus contributing to the uniformity of the programing and facilitating treatment of the problem by modern digital computing machines. Hansen's original lunar theory requires the use of the derivatives of the disturbing function with respect to the eccentricity and the parameters determining the orbit plane's position. This means that a "literal" development of the disturbing function must be obtained before the "numerical" values of the elements can be substituted. The present modification permits a numerical development of the disturbing function. In order to reproduce some of Hansen's series, the author developed methods for the computer to perform both numerical and algebraic operations. The trigonometric series employed in the lunar problem are slowly convergent. The original program allowed 50 terms to a series. Of the two completed versions, the program written for the IBM7094 Mod II allows for 200 terms to a series and the Univac 1107 version allows 3333 terms to a series. The IBM 7094 program utilizes the double core storage of 65,000 words. The Univac 1107/8 program uses 500,000 words of drum storage and allows 10,000 words of storage for each series. Almost the entire 65,000-word core storage of the Univac 1107/8 is used as accumulators to bring in the series to be operated on and to accumulate the results. Core storage of 20,000 words is used as an accumulator to store the resultant series. A complete package of routines to multiply, add, subtract, scalar multiply, differentiate, integrate, and evaluate trigonometric series and to extract the numerical coefficient of any argument was written. By the uses of these tools, series operations are programed almost as easily as numerical calculations. The foregoing is a technical description of the program employed. I also would like to discuss the history of this continuing effort. Analytic solutions to orbit problems were pursued by P. Musen at the Goddard Space Flight Center in 1959 and 1960. It was suggested that if we could multiply A sm(IX) -fB sin(JY), where A, B, I, and J are numbers and X and Y are "literals," analytic theories could be calculated using digital computers. These original efforts have led to the present programs. Some of the mistakes in the program were extremely difficult to correct. As an example, a discrepancy in the calculation of n$y (the motion of perigee of the moon) was not corrected until we returned to the problem after suspending it for a period of six to eight months. Further efforts will be in the direction of additional improvement of the Jupiter X orbit through differential correction and the calculation of the orbits or other Jupiter satellites which are also strongly perturbed. Some of the results of the differential correction process as applied to Jupiter X are included as Tables 1 and 2. The difference between observation and prediction is of the order of 2 sec of arc.

Behavior of turbulent flow near a porous wall with pressure gradient

Abstract: : Van Driest's theory, which provides a continuous velocity and shear distribution for turbulent flow near a nonporous wall, is extended to turbulent flow near a porous wall. The new, modified theory enables the theoretical calculation of velocity profiles to be performed for a wider range of mass- transfer rates, and it gives good agreement with experimental data.

Transonic flowfield in a supersonic nozzle with small throat radius of curvature.

Abstract: Internal flow measurements in transonic region of supersonic nozzle with small throat radius of curvature compared with prediction data

Static and dynamic applications of a high- precision triangular plate bending element

Abstract: A fully conforming plate bending element of arbitrary triangular shape is developed and applied to the solution of several static and dynamic plate problems. The element incorporates 18 generalized coordinates, namely the transverse displacement and its first and second derivatives at each vertex. Example applications presented include static and dynamic analyses of a square plate with edges either simply supported or clamped, statics of an equilateral triangular simply supported plate, and vibrations of cantilevered triangular plates. Rates of convergence of the finite element approximations are investigated both theoretically and numerically. Excellent accuracy is achieved in all cases, and the rates of error convergence agree closely \vith predicted asymptotic values.

A rapidly converging triangular plate element

Abstract: Compatible triangular plate elements for normal and in-plane displacements, discussing nine degree of freedom element, strain energy, simply supported and clamped plates

A Method for Extracting Aerodynamic Coefficients from Free-Flight Data

Abstract: Aerodynamic coefficients from observed motion of body in flight, eliminating need for closed form solutions by employing numerical solutions to equations of motion

A survey of impulsive trajectories.

Abstract: Impulsive trajectories optimal and nonoptimal solutions, classifying known results for reference purposes

Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit.

Abstract: Minimum fuel multiple impulse orbital rendezvous for fixed transfer time near circular orbits

Measurements and Correlations of Transition Reynolds Numbers on Sharp Slender Cones at High Speeds

Abstract: : An experimental investigation of laminar boundary-layer transition on a sharp, 10-deg total-angle, insulated cone at zero yaw was conducted in 12- and 40-in. supersonic wind tunnels at free-stream Mach numbers from 3 to 6. This research was directed toward defining the relationship between the aerodynamic noise disturbances and boundary-layer transition Reynolds numbers in high-speed wind tunnels and extended previously published planar results to include axisymmetric models. A significant increase in the Reynolds numbers with increasing tunnel size (similar to the planar results) is shown to exist. Sharp cone transition Reynolds numbers from ten facilities (12- to 54-in.) for free- stream Mach numbers from 3 to 14 and a unit Reynolds number per inch range from 100,000 to 1,200,000 were correlated using aerodynamic-noise-transition parameters. A quantitative correlation of the ratio between cone and planar Reynolds numbers values was developed which demonstrates a strong Mach number dependence and also indicates a variation with tunnel size and unit Reynolds number.

Viscous Shock Layer at the Stagnation Point with Nonequilibrium Air Chemistry

Abstract: A finite-difference method and a nonlinear overrelaxation method are investigated for solving the viscous shock layer at the stagnation point of a blunt body. An air gas model is employed with finite reaction rates and accurate thermodynamic and transport properties. For a body with a 1-in. nose radius and at a velocity of 20 kfps, the present results at 100, 150, 200, and 250 kft show that boundary-layer theory with the inviscid edge flow in chemical equilibrium is appropriate for some altitude below 150 kft. When the altitude is 250 kft, the effects of shock slip must be included in the viscous shock-layer solution. For this case, the air is only slightly dissociated and ionized. The present results, with a seven-species air model, are in general agreement with the diatomic air model results of Cheng and Chung.

Nonlinear flutter of curved plates.

Abstract: Nonlinear Galerkin analysis of curved plate flutter, using shallow shell/von Karman equations and quasi-steady aerodynamic theory

Axisymmetric dynamic snap-through of elastic clamped shallow spherical shells.

Abstract: The behavior of axisymmetric dynamic snap-through of elastic, clamped shallow spherical shells under a uniform pressure has been investigated by.several authors. In most of the previous work, approximate methods were used, and as yet no positive conclusion has been made on the critical load for snap-through. In this paper, a numerical method is developed for solving the governing nonlinear differential equations of this problem. Two types of loading conditions are included-—an impulsive load and an instantaneous ly applied step load with infinite duration. In the case of impulsive loading, it is found from the quasi-static problem under zero load that the only equilibrium, position of the shell is its undeformed configuration. Hence, if we define the dynamic snap-through based on the finite jump behavior of deflection then there is no possibility for dynamic snap-through under impulsive loading. In the case of step loading, the snap-through loads are evaluated for a wide range of the geometrical parameter of the shell. Comparison of the present calculated critical loads with the previous results from approximate methods is made. It is found that the present critical load checks closely with an experimental value of the critical load for one value of the geometrical parameter of the shell.

Finite element analysis of inelastic structures.

Abstract: Differential stress-strain relationships are used to generate a system of simultaneous firstorder differential force-displacement equations which are integrated numerically to obtain the stresses, strains, and displacements in inelastic structures. For the biaxially stressed element, the concept of isotropic hardening and a generalized stress are used to evaluate an effective modulus and Poisson's ratio, which vary continuously from their initial values during elastic straining action to their asymptotic values during intense plastic straining action. The surface of plasticity for this element closely approximates the von Mises surface when the generalized stress is set equal to the von Mises stress and the strain distribution is essentially identical to that obtained by the Prandtl-Reuss incremental flow theory. The analysis of the MIT shear lag structure is presented to demonstrate the applicability of the method to systems of practical size and interest. Nomenclature A = equilibrium matrix B = compatibility matrix C = stress-strain matrix C = differential stress matrix E = Young's modulus Et = tangent modulus Es = secant modulus K — stiffness matrix K = differential stiffness matrix P = applied load parameter u = element nodal displacements X = element nodal forces X = load constant n = Poisson's ratio fjLt = tangent Poisson's. ratio Us = secant Poisson's ratio e = strain a- = normal stress

Axisymmetric static and dynamic buckling of spherical caps due to centrally distributed pressures

Abstract: Spherical caps axisymmetric static and dynamic buckling under load, using axisymmetric nonlinear elastic shell theory approximation and finite difference equations

An engineering survey of radiating shock layers.

Abstract: John Anderson received his Bachelor of Aeronautical Engineering Degree from the University of Florida in 1959 and his PhJD. in Aeronautical and Astronautical Engineering from Ohio State University in 1966. From 1959 to 1962, Dr. Anderson served as a Lieutenant and Task Scientist in the U.S. Air Force at the Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio. At Ohio State University from 1962 to 1966, he studied under National Science Foundation and NASA graduate fellowships. Since 1966, Dr. Anderson has been Chief of the Hypersonics Group, Aerophysics Division, at the U.S. Naval Ordnance Laboratory, White Oak, Maryland. Also since 1966, he has been a Lecturer in the Mechanical Engineering Department at Catholic University. Dr. Anderson is a member of Tau Beta Pi, Sigma Xi, Sigma Tau, AIAA, and the American Physical Society. He has published in the areas of radiation gas dynamics, high-temperature nonequilibrium flows, and hypersonic aerodynamics. "In science, by a fiction as remarkable as any to be found in law, what has once been published, even though it be in the Russian language, is spoken of as known, and it is too often forgotten that the rediscovery in the library may be a more difficult and uncertain process than the first discovery in the laboratory.)J Lord Raykigh—1884

Buckling of axisymmetric imperfect circular cylindrical shells under axial compression

Abstract: Circular cylindrical shells with axisymmetric imperfections tested under axial compressive load, studying imperfection amplitude and wavelength effects on minimum buckling load

Calculation of nonequilibrium hypersonic turbulent boundary layers and comparisons with experimental data

Abstract: Compressible hypersonic turbulent boundary layers solution by finite difference method, relating mixing length to velocity profile shape factor