The paper deals with a class of shock-wave systems that are of importance in the design and operation of supersonic intakes. It is shown that, when n− 1 wedge shocks, all of the same family, meet at a point, together with a tail shock and a bow shock, then the equations of motion which describe the flow near the shock confluence or junction are reducible to a polynomial equation of degree 10. Numerical results are obtained for the special case of the four-shock confluence and it is shown that, the number of solutions of physical interest, m4, may be 0, 2 or 4. It is found that the m4=0 solution can be interpreted physically in three different ways. These are a Guderley type flow, a confluence of three shocks with a Prandtl-Meyer expansion fan or the appearance of a shock system containing more than one confluence point. The methods developed also permit the discussion of multi-confluence wave systems and a number of examples are given. Finally, the Prandtl-Meyer compression fan is brought within the scope of the method by approximating it with a system of shock waves of weak intensity and minimum entropy.

The paper treats the general problem of the response to multiple random excitation of a system having n degrees of freedom. Analysis is developed which connects the spectral density matrix of a set of generalised coordinates with that of corresponding generalised forces, and makes explicit the contributions of the various normal modes. The case of two degrees of freedom is considered in detail. The importance of cross-correlations between modes is shown by determining their effects on spectra and on mean-square response.

Jet drag, defined as the form drag associated with jet entrainment in otherwise inviscid fluid, has been analysed by replacing a two-dimensional incompressible jet with a suitable continuous distribution of sinks. Exact solutions for the jet drag, with the flow incompressible and the jet turbulent, are presented for uncambered struts of various shapes (including an ellipse and a circular cylinder), various thickness ratios, and with blowing slots of various widths in both quiescent and uniform streaming flow. In uniform streaming flow the jet is blowing in the direction of the external flow. The extension of the theory to cross-stream blowing (as in the jet flap) is discussed.

The present theory compares favourably with the few available experimental results when the ratio of jet velocity to streaming-flow velocity is sufficiently large.

This paper contains a theoretical study for an idealised ground effect wing, both tips of which are close to the ground. The wing is assumed to be a simple semicircular lifting line in a transverse plane and the fluid is assumed incompressible and inviscid. When the gap between the tips and the ground tends to zero, the flow velocity through it becomes infinite. This fact is unrealistic and seems to be the reason why the theoretical ground effect is in error.

Non-symmetric response of elastic shells to localised impact loads is studied. Closed-form solutions for the response to four particular kinds of pulse shapes are given. Experimentally measured values of the strain response of a cylinder to impact loads are obtained which compare satisfactorily with theoretical predicted values.

A procedure is developed for the analysis of plane stress problems when yielding occurs locally. The region is divided into triangular elements and the deformation is analysed on a step-by-step basis, using the matrix notation developed by Argyris. The simple expressions which are derived for the element properties are applicable with any stress-strain relations which are stable and time-independent. Simple numerical examples are given.