The post-buckling behaviour of flat square plates loaded along two opposite straight edges is analysed using the von Kármán equations, trigonometric series and Galerkin’s method. The unloaded edges are considered to be either free to distort in the plane of the plate or maintained straight but allowed to move bodily; all edges are simply-supported in the out-of-plane direction. The non-linear algebraic equations are solved approximately using a McLaurin’s series expansion technique which facilitates the development of explicit expressions for ultimate load, end shortening and stiffness. The effects of initial geometric imperfections are also studied and it is shown that the results for ultimate load prediction and end shortening are in good agreement with test results.

The attitude dynamics of a spinning satellite containing an elastically-restrained, viscously-damped mass, is investigated. This non-rigidity approximately represents the interesting practical case of equipment supported by relatively soft anti-shock mountings and the case of a particular viscous nutation damper. The linearised differential equations and the transfer functions relating the dynamic behaviour of the oscillating mass to the spinning-body components of the angular speed and the external torque are determined. On these grounds, the possibility of unstable configurations is singled out and discussed, and the stability condition is established, within the small perturbation approximations. Furthermore, the attitude dynamics for the satellite, both for large manoeuvres and fine corrections, is obtained by applying a train of pulsed torques by means of a suitable control logic and mass-ejection jets. The results are compared with those obtained from rigid-body theory. It is demonstrated that comparatively wide nutations may be produced, and the influence of the relevant parameters is determined.

Spanwise velocity correlations of the turbulent vortices shed by a two-dimensional bluff body of D-section are presented for different aspect ratios of the shedding body between end-plates. From these it is shown that the vortices are only shed two-dimensionally when the gap between the end-plates is less than or equal to four times the base height of the shedding body.

The transient motion of a shock wave is investigated during its passage through ducts containing various area convergences. The method of characteristics has been used to follow the unsteady motion of the shock wave in an inviscid, non-conducting gas. The strength of the shock is taken to be large enough so that initially both sets of characteristics face downstream. The results are found to be in good agreement with unsteady and quasi-steady theories. A comparison is made between the characteristics results and experimental results obtained in a 1 ft (0·305 m) diameter shock tube. This shock tube incorporates a 3·75:1 linear area change in the low pressure section length. Good agreement is found between experiment and theory. A comparison is also made with other experimental work.

Steady, constant-density, two-dimensional flow in a laminar boundary layer is considered over a permeable curved surface, for conditions such that the equation of motion has similar solutions. Account is also taken of the displacement of the main stream by the boundary layer.

Integration of the equation of motion on a digital computer yields results indicating that, for given values of curvature and longitudinal pressure gradient, suction reduces the boundary-layer thickness and increases skin friction. Blowing has the reverse effects. The amount of suction or blowing required to produce neutral stability is independent of curvature and so may be deduced from data for flat surfaces.

For a given curvature, blowing reduces, whereas suction increases, the magnitude of the adverse pressure gradient which the boundary layer can withstand before separation occurs. For a surface through which there is blowing or only a small amount of suction, convex curvature also reduces the magnitude of the adverse pressure gradient producing separation; but for larger amounts of suction the effect of surface curvature on separation is reversed.

Using a modified model of the axially-loaded Timoshenko beam, nine field transfer matrices for the homogeneous case and three field matrices for the non-homogeneous case have been derived, covering thus all the “cases of state” of continuous beams loaded axially and laid on an elastic foundation. The loads and restraints (translatory and rotatory) may be both concentrated and distributed. The matrices make possible a simultaneous treatment of free vibrations, forced vibrations, statics and buckling.