Asymptotically almost periodic solutions of a nonlinear Volterra system
Nonlinear Volterra integral equation system solution using almost periodic forced oscillations
Miller, R. K.↗
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Elastic cracks and screw dislocation pile-ups crossing a bimaterial interface
Elastic cracks and screw dislocation pile-ups crossing bimaterial interface, deriving dual singular integral equations
Chou, T.-W.↗
Lifting-surface theory for calculating the loading induced on a wing by a flap
A method is described for using lifting-surface theory to obtain the pressure distribution on a wing with a trailing-edge flap or control surface. The loading has a logarithmic singularity at the flap edges, which may be determined directly by the method of matched asymptotic expansions. Expressions are given for the singular flap loading for various flap hinge line and side edge geometries, both for steady and unsteady flap deflection. The regular part of the flap loading must be obtained by inverting the lifting-surface-theory integral equation relating the pressure and the downwash on the wing: procedures are described to accomplish this for a general wing and flap geometry. The method is applied to several example wings, and the results are compared with experimental data. Theory and test correlate well.
Johnson, W. A.↗
Prediction of unsteady aerodynamic loadings caused by trailing edge control surface motions in subsonic compressible flow: Analysis and results
A theoretical analysis and a computer program have been developed for the prediction of unsteady lifting surface loadings caused by motions of trailing edge control surfaces having sealed gaps. The final form of the downwash integral equation has been formulated by isolating the singularities from the non-singular terms and establishing a preferred solution process to remove and evaluate the downwash discontinuities in a systematic manner. Comparisons of theoretical and experimental pressure data are made for several control surface configurations. The comparisons indicate that reasonably accurate theoretical pressure distributions and generalized forces may be obtained for a wide variety of control surface configurations. Spanwise symmetry or antisymmetry of motion, and up to four control surfaces on each half span can be accommodated.
Rowe, W. S.↗
A selective review of ground based passive microwave radiometric probing of the atmosphere
The absorption of the various atmospheric constituents with significant microwave spectra is reviewed. Based on the available data, an estimate is made of the uncertainty in the microwave absorption coefficients of the major constituents, water vapor and oxygen. Then there is an examination of the integral equations which describe the three basic types of observations: measurement of the spectrum of absorption of the sun's radiation by an atmospheric constituent, measurement of the emission spectrum of a constituent, and measurement at one frequency of the zenith angle dependence of the absorption or emission of the atmosphere.
Welch, W. J.↗
Two-dimensional finite-element temperature variance analysis
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Heuser, J. S.↗
A theoretical study of radar return and radiometric emission from the sea
The applicability of the various electromagnetic models of scattering from the ocean are reviewed. These models include the small perturbation method, the geometric optics solution, the composite model, and the exact integral equation solution. The restrictions on the electromagnetic models are discussed.
Peake, W. H.↗
On backscatter from spatially varying surfaces
The theory of radar backscatter from rough (spatially varying) surfaces is discussed. An integral equation developed to describe the radar backscatter from a perfectly conducting surface is applied to nonsmooth surfaces. The results are compared with those obtained by Beckmann as well as those obtained by Wright. Differences between the three solutions are discussed.
Grody, N. C.↗
Hypersonic bodies of maximum drag for a given lift-to-drag ratio.
The problem considered in this paper is concerned with the aerodynamic design of the forebody shape of reentry vehicles in the blunt, homothetic, elliptic transversal contour, power-law longitudinal contour, raked-off configurational set. In particular, the forebody shape which maximizes the ratio of the forebody pressure drag to the free-stream dynamic pressure for a given lift-to-drag ratio and given geometric properties is determined. This problem is considered because recent survey articles indicate that its solution will provide useful qualitative design information about manned vehicles entering the earth's atmosphere from any of the foreseeable planetary missions. Single-integral equations relating the lift and drag in Newtonian hypersonic flow to the forebody geometry are derived and used to formulate the optimization problem which is solved by a direct numerical method.
Mcmillan, W., III↗
The problem of an elastic stiffener bonded to a half plane.
The contact problem of an elastic stiffener bonded to an elastic half plane with different mechanical properties is considered. The governing integral equation is reduced to an infinite system of linear algebraic equations. It is shown that, depending on the value of a parameter which is a function of the elastic constants and the thickness of the stiffener, the system is either regular or quasi-regular. A complete numerical example is given for which the strength of the stress singularity and the contact stresses are tabulated.
Erdogan, F.↗
Pressure losses for laminar flow in the entrance region of ducts of rectangular and equilateral triangular cross section.
The velocity profiles upon which the pressure-loss calculations are based, are recomputed using the previously described method of reference (1960). The pressure drop is then computed using the energy integral equation; both rectangular and equilateral triangular ducts are considered. It is demonstrated that, using this equation, the pressure-drop parameter can be improved.
Miller, R. W.↗
Reduction of the Dirichlet problem to an initial value problem.
Although the derivation is concerned with solutions for plane regions with prescribed boundary values, the approach presented could by easily generalized to higher dimensions. The initial-value method is derived by a combination of invariant imbedding techniques and the Fredholm integral equation method of representation of the potential as a function of a dilayer distribution on the boundary of the region in question.
Kalaba, R.↗
Radiation from a parallel-plate waveguide into a dielectric or plasma layer.
An analytical solution for radiation from a truncated parallel-plate waveguide into a dielectric or plasma slab is obtained by solving the Hilbert problem associated with a certain singular integral equation. The technique has the advantage that the edge condition is easily shown to be satisfied, and numerical results can be obtained with excellent accuracy. Numerical results are presented for a variety of dielectric and plasma slabs, parallel-plate separations, and aperture-to-slab distances.
Kostelnicek, R. J.↗
Penny-shaped interface crack between an elastic layer and a half space.
The axially symmetric elastostatic problem for a layer bonded to a half space with different material properties is considered. It is assumed that the bi-material interface contains a penny-shaped crack the surfaces of which are subjected to known tractions. The solution of the problem is reduced to that of a system of singular integral equations of the second kind. A numerical example for an aluminum-epoxy material combination is given. The stress intensity factors and the strain energy release rate are calculated and are given as functions of layer thickness-to-crack radius ratio.
Erdogan, F.↗
A circumferential crack in a cylindrical shell under torsion.
The fully antisymmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.
Erdogan, F.↗
Stresses near a flat inclusion in bonded dissimilar materials.
The plane elastostatic problem for bonded materials containing a flat inclusion is considered. It is assumed that the inclusion is located parallel to or on the interface and may be rigid or elastic with negligible bending rigidity. The integral equations for various cases are derived and their solutions are described. The stress state around the singular points are investigated and a pair of stress intensity factors similar to that for crack problems are defined. A series of numerical examples for two bonded half planes and for a half plane is worked out. The stress intensity factors are presented as functions of the ratio of the distance from the interface to the length of the inclusion.
Erdogan, F.↗
Turbulent boundary layer on a rotating helical blade.
Investigation of the boundary-layer characteristics on a helical blade of large chord length, enclosed in an annulus and rotating in a fluid otherwise at rest. The three-dimensional form of momentum integral equations is derived, and is used to predict the boundary-layer growth and limiting streamline angles on the blade surface. The measurements are in general agreement with the predictions. The wall shear stress correlation, which includes both Reynolds number and rotation parameters, valid for a rotating blade operating at zero pressure gradient, is derived. Radial and tangential velocity profiles, the tangential component of turbulence intensity, and blade static pressures are measured at several locations on the blade surface. The nature of flow near the blade tip is discussed. An expression for the radial velocity profile, valid in the outer region of the boundary layer, is derived theoretically.
Lakshminarayana, B.↗
Nonlinear actuator disk theory.
Results obtained from a recent investigation of the flowfield induced by a heavily loaded actuator disk. First, the governing nonlinear integral equations are formulated from two different points of view, and the iterative solution is briefly outlined. Calculated flow patterns are presented for representative advance ratios and blade circulation distributions. For the static condition, the experimentally observed lingering of the tip vortices in the propeller plane, and the insensitivity of the streamline pattern to thrust coefficient are both accounted for, and a 'dividing streamline' - apparently not previously discussed in the literature, is predicted for the nonstatic case. Finally, the relationship between the actuator disk flow and the zero harmonic of the flowfield induced by a finite-bladed propeller is considered.
Greenberg, M. D.↗