Showing papers in "Quarterly Journal of Mechanics and Applied Mathematics in 1982"

Diffraction by a finite strip

Abstract: A new approach is presented to diffraction problems involving plane strip barriers or slit apertures. These are problems that display the effects of multiple interacting edges. The approach taken here provides exact, compact solutions. The theory is introduced through a series of examples that are, in fact, the 'standard' problems of the subject, diffraction of a plane oblique wave by a slit, for example. In each case, the solutions are found to depend explicitly on a single 'special' function and its Fourier transform. These fundamental functions are described, with the emphasis placed on practical computational methods. The example problems are all couched in the language of acoustics.

Indentation of an elastic half-space by a cooled flat punch

Abstract: SUMMARY A solution is given for the frictionless thermoelastic contact of a cooled flat cylindrical rigid punch and an elastic half-space. If the thermal distortion is sufficiently small, contact is retained over the entire punch face and the solution can be written down from known results. For larger temperature differences the conventional boundary conditions do not permit a solution, but a solution is here developed in which a central circle is in imperfect contact, i.e. a non-zero contact resistance exists between the surfaces. The problem is reduced to a boundary-value problem in potential theory using a solution of the thermoelastic equations in two harmonic functions. These functions are written as the sum of a number of components each of which satisfies two-part boundary conditions. The resulting boundary conditions lead to coupled Abel integral equations which are reduced to a single Fredholm equation by substitution. Results are given for typical contact pressure distributions and for the relationship between load, temperature difference, heat flux and the radius of the imperfect contact region.

Stability of two-dimensional natural convection in a porous layer

Abstract: Etude des conditions dans lesquelles apparait la transition d'un ecoulement laminaire a un ecoulement fluctuant. On utilise la methode de Galerkin pour etudier la convection tridimensionnelle dans un cube

The external axisymmetric interface crack with heat flow

Abstract: Two half-spaces of dissimilar material properties are brought together and bonded over a circular region of radius r = a to form an exterior axisymmetric interface crack. Loads are applied at infinity such that the common boundary (i.e. the bond and any contact region that develops) transmits tractions whose resultant is an axial tension P. Interpenetration is predicted if the track is assumed to be completely open; in fact an annular contact region {a b. If the temperatures of the bodies are now changed, the extent of this contact region changes. A solution to this problem is obtained by representing the displacement in the bodies in terms of harmonic potential functions and reducing the resulting mixed boundary-value problem to an integral equation which is solved numerically. Detailed results are given for the particular case in which both bodies are raised to the same temperature. If the load P is zero, the crack either closes completely or opens almost completely, depending on the sign of certain combinations of physical constants. Results are also given for the case where one body is a rigid perfect conductor and the other is maintained at zero temperature.

Solution of the unsteady subsonic thin airfoil problem

Abstract: The problem of a thin airfoil subject to simple harmonic disturbances in a uniform subsonic free stream is solved by extension of a technique developed earlier for a stationary strip vibrating in a uniform fluid. Explicit expressions are given for the lift and moment, acoustic directivity pattern, and total acoustic power for arbitrary upwash and, in particular, for the 'elementary disturbances': plunge, pitch and a stationary transverse gust. Numerical results for a simple skewed gust are presented and compared to the high-frequency asymptotic theory of Martinez and Widnall.