Bonded elastic half-planes with an interface crack and a perpendicular intersecting crack that extends into the adjacent material. I, II
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Goree, J. G.↗
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Solution of several problems for doubly connected regions with contiguous circular boundaries
Mathematical solution for doubly-connected regions with contiguous circular boundaries, and treatment of half-plane with one circular hole and plane with two equal holes
BOUNDARY VALUE↗
On the Michailov criterion for exponential polynomials.
Michailov criterion for exponential polynomials, determining existence of zeros in right half-plane
AUTOMATIC CONTROL↗
The effect of shear modulus on the stress distribution produced by a planar array of screw dislocations near a bi-metallic interface.
Shear modulus effect on stress distribution of planar array of screw dislocations near bimetallic welded half-planes interface
SCREW DISLOCATION↗
Three-dimensional crack problems
Methods for solving three dimensional crack problems are discussed. The stress intensity factor for the case of uniform pressure on the surface crack is analysis. An analysis of concentrated forces acting on the crack faces parallel to the crack front of a half-plane crack was made. Two dimensional calculations were made using the exact solution for the stress field around an elliptical hole in a uniformly stretched plate. The strain energy density was computed in the neighborhood of the ends of narrow, but sharp, ellipses.
Hartranft, R. J.↗
Antiplane shear crack terminating at and going through a bimaterial interface
The antiplane shear problem of two bonded elastic half-planes containing a crack perpendicular to the interface is considered. The cases of a semiinfinite crack terminating at the interface, a finite crack away from and terminating at the interface, two cracks one on each side of the interface, and a finite crack crossing the interface are separately investigated. The nature of the stress singularity for the crack terminating at and going through the interface is studied, and it is shown that at the irregular point on the interface, for the former the power of singularity is not -1/2 and for the latter the stresses are bounded. For a material pair of aluminum-epoxy some numerical results giving the stress intensity factors, the density functions, and the crack opening displacements are presented.
Erdogan, F.↗
An orthotropic laminate composite containing a layer with a crack
A laminate composite containing an orthotropic layer with a crack situated normal to the interfaces, and bonded to two orthotropic half-planes of dissimilar materials was considered. The solutions for two different classes of orthotropic materials are presented. In each case, the problem was first reduced to a system of dual integral equations, then to a singular integral equation which was subsequently solved numerically for the stress intensity factors at the tip of the crack. The effect of the material properties on the stress intensity factor was investigated. The generalized plane stress and the plane strain were treated simultaneously.
Arin, K.↗
Three-dimensional growth characteristics of a plane crack subjected to concentrated forces
A combination of longitudinal shear and normal forces acting on a half-plane crack is shown to lead to predictions of crack growth qualitatively similar to those obtained by Knauss (1970) for crack propagation in antiplane shear. The presented results, based on the strain-energy-density fracture criterion, predict the direction of growth and the load which initiates it.
Hartranft, R. J.↗
Stability criteria for two-variable polynomials
Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in a finite number of steps. Stability is tested with respect to either the half-plane or the unit circle applying only two times the equivalent of the Routh or Marden test, regardless of the degree of the polynomial.
Siljak, D. D.↗
Crack growth in bonded elastic half planes
Two solutions were developed for the two dimensional problem of bonded linearly elastic half-planes. For each solution, numerical results are presented for the stress intensity factors, strain energy release rate, stresses, and displacements. The behavior predicted by the studies was investigated experimentally using polymers for the material pairs. Close agreement was found for the critical stress intensity factor at fracture for the perpendicular crack near the interface. Fracture along the interface proved to be inconclusive due to difficulties in obtaining a brittle bond. Some interesting and predictable behavior regarding the potential for the crack to cross the interface was observed and is discussed.
Goree, J. G.↗
An orthotropic laminate composite containing a layer with a crack
A laminate composite containing an orthotropic layer with a crack situated normal to the interfaces, and bonded to two orthotropic half-planes of dissimilar materials, is considered. The solutions for two different classes of orthotropic materials are presented separately. In each case, the problem is first reduced to a system of dual integral equations, then to a singular integral equation which is subsequently solved numerically for the stress intensity factors at the tip of the crack. The effect of the material properties on the stress intensity factor is investigated. Two cases, the generalized plane stress and the plane strain, are treated simultaneously.
Arin, K.↗
Characteristics of the unsteady motion on transversely sheared mean flows
An explicit representation for the unsteady motion on a transversely sheared mean flow is obtained which corresponds to the gustline motion on a uniform mean flow. The important features of this motion are discussed. It is shown that its velocity, pressure and vorticity are all induced by a certain disturbance field that is a linear combination of the vorticity and particle-displacement fields and is everywhere frozen in the mean flow. The general ideas are illustrated by considering the scattering of a gust by a half-plane embedded in a shear flow.
Goldstein, M. E.↗
Applications of diffraction theory to aeroacoustics
A review is given of the fundamentals of diffraction theory and the application of the theory to several problems of aircraft noise generation, propagation, and measurement. The general acoustic diffraction problem is defined and the governing equations set down. Diffraction phenomena are illustrated using the classical problem of the diffraction of a plane wave by a half-plane. Infinite series and geometric acoustic methods for solving diffraction problems are described. Four applications of diffraction theory are discussed: the selection of an appropriate shape for a microphone, the use of aircraft wings to shield the community from engine noise, the reflection of engine noise from an aircraft fuselage and the radiation of trailing edge noise.
Lansing, D. L.↗
Applications of diffraction theory to aeroacoustics
The fundamentals of diffraction theory were reviewed and applied to several problems of aircraft noise generation, propagation, and measurement. The general acoustic diffraction problem is defined and the governing equations were set down. Diffraction phenomena are illustrated using the classical problem of the diffraction of a plane wave by a half-plane. Infinite series and geometric acoustic methods for solving diffraction problems are described. Four applications of diffraction theory are discussed: the selection of an appropriate shape for a microphone, the use of aircraft wings to shield the community from engine noise, the reflection of engine noise from an aircraft fuselage, and the radiation of trailing edge noise.
Lansing, D. L.↗
On the output of acoustical sources
Contents: (1) a theoretical basis for local power calculation; (2) source radiation in the presence of a half-plane; (3) radiation from a line source near an edge at which a Kutta condition holds; (4) radiation by a point source above a plane independence boundary; and (5) power output of a point source in a uniform flow.
Levine, H.↗
Output of acoustical sources
Acoustic radiation from a source, here viewed as an immobile point singularity with periodic strength and a given multipolar nature, is affected by the presence of nearly structural elements (e.g., rigid or impedance surfaces) as well as that of a background flow in the medium. An alternative to the conventional manner of calculating the net source output by integrating the energy flux over a distant control surface is described; this involves a direct evaluation of the secondary wavefunction at the position of the primary source and obviates the need for a (prospectively difficult) flux integration. Various full and half-planar surface configurations with an adjacent source are analyzed in detail, and the explicit results obtained, in particular, for the power factor of a dipole brings out a substantial rise in its output as the source nears the sharp edge of a half-plane.
Levine, H.↗
The radiation of sound by the instability waves of a compressible plane turbulent shear layer
The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.
Tam, C. K. W.↗
Extension of oblique incidence method to photo-orthotropic-elasticity
With the interpretation of isochromatic and isoclinic fringes in transparent, birefringent, orthotropic composites established, efforts were in progress to determine the individual values of the principal stresses or strains. Several methods utilize the photoelastic results only partially and rely on numerical procedures. Others attempt to obtain the required information based entirely on experimental data. The classical oblique incidence technique as applied to transversely isotropic birefringent composites, is presented. The proposed extension is verified by applying it to the problem of an orthotropic half-plane subjected to an edge-load.
Prabhakaran, R.↗