The work described in this paper forms part of a programme on the local buckling of long thin flat-walled structures, such as integrally stiffened panels or corrugated core sandwich panels, with the individual flats subjected to combined longitudinal compression and shear. When buckling occurs, the line junctions between adjoining flats remain straight, but rotations occur about the junctions. These rotations vary sinusoidally in the longitudinal direction but, because of the shear, the rotations at the two edges of an individual flat are out of phase with each other. In order to picture the buckling mode it is essential to have at least a qualitative idea of the shape of the nodal lines in the flats. The analysis of this paper is entirely concerned with this problem.

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.

Drag measurements were made on a blunt-based body of revolution with the addition of several alternative boat-tailed afterbodies. The best of these afterbodies, with a length of only 60 per cent of the maximum diameter, gave almost as much reduction of drag as a conventional streamline tail. The pressure distribution on this body was measured for various lengths. It does not seem to be possible at present to predict quantitatively the drag of this type of body but some qualitative design principles have been suggested.

Wind tunnel measurements have been made of the attachment-line boundary layer on a swept wing. The combination of a 4-5 in (114 mm) nose radius and 60° angle of sweep enabled a wide range of values of the parameter V2/(v dU/dx) (denoted here by C*), to be covered, and gave a thick enough boundary layer for the velocity profiles to be accurately measured. Pitot traverses were performed for values of C* from 0·59 × 105 to 3·7 × 105. Without a trip wire fitted the attachment-line flow was laminar over the full range and the measured velocity profiles agreed closely with the theory for an infinite swept wing. With a large trip wire fitted, a transition régime was observed in the range 0·6 × 105 < C* < 1·4 × 105, and at higher values of C* the flow was fully turbulent and showed good agreement with the earlier calculations of Cumpsty and Head. Preston tubes were used for skin friction measurements in fully turbulent conditions and a hot wire was used to explore the development of turbulence in the transition régime.

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.

The discrete element displacement method is used to analyse the instability of flat rectangular plates subjected to arbitrary systems of in-plane loading. Critical load intensities calculated in a range of applications, some of which include discrete reinforcing members, are compared with the predictions of past investigators and demonstrate the accuracy of the procedure.

The main purpose of this paper is to illustrate the use of the stability functions for long plates in combined compression and shear defined in a previous paper by the authors. The panel is supported on its two edges and on a series of N intermediate simple supports. Each of the two edges is either clamped or simply-supported and numerical results are given for each of the three possible combinations, with varying numbers of supports. In all cases it is found that a simple parabolic interaction formula between shear and compression is extremely accurate. Also simple approximate formulae are given for calculating the wavelength of the buckle and the lead of the nodal lines for any combination of compression, shear, edge conditions and number of supports.

This paper presents a method with strong convergence characteristics for the determination of eigenvalues and eigenvectors of continuous systems. The limitation on the number of undetermined constants in the displacement functions introduced by the conditions at the ends of a segment is removed by the introduction of points of freedom within the segment.

This improves the convergence of eigenvalues and eigenvectors very rapidly with the number of segments, especially in torsional vibration problems where the convergence with the usual Matrix Displacement method is very poor. The continuous medium is successively approximated by the use of sub-systems with finite numbers of degrees of freedom. The principles upon which the method is based and the convergence of the results are discussed and illustrated by a series of examples.

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 displacement effects on a set of five rectangular mouthed pitot tubes of a constant thickness ratio, 0-6, were investigated in fully developed turbulent flow in a plain tube. The results show that the displacement due to shear only, δ1, is given by δ1/b=0.19, where b is the outside thickness of the pitot tube. The additional wall effect is found to have a dependence on Reynolds number or, equivalently, wall shear within the range investigated of 27 500 < Rev < 58 300. The wall effect results may be presented as a single curve, however, if consideration is given to the distance up to which the wall effect is present.

A method for calculating the growth of a turbulent wall jet in streaming flow has been developed. The flow is assumed to be two-dimensional, incompressible and over a plane, smooth wall. Downstream variations of pressure are permitted and separation in an adverse pressure gradient may be predicted. The method incorporates procedures for matching the flow to that at the blowing slot, although it is postulated that the upstream boundary layer there is thin enough that the wall jet develops without an unmixed wake (i.e. there is not a minimum in the mean-velocity profile).

The method incorporates four integral momentum equations taken from the wall to various points in the flow. The calculation of the outer shearing stress, although empirical, is based on the large-eddy equilibrium hypothesis and therefore has some foundation. The remaining empiricism in the method is based on measurements in self-preserving wall jets.

The method has been used to predict the jet-momentum coefficient required to suppress separation over a trailing-edge flap attached to a thin aerofoil. Plausible curves have been obtained Using assumed values of upstream boundary layer at the slot. Of some practical interest is the indication that large savings in power are possible if the upstream boundary layer is removed. This indicates that blowing combined with upstream suction, or multiple-slot blowing, may give useful savings in the application of blowing to prevent separation.

This paper deals with the effects of a superimposed radial outflow upon the motion of the fluid between a rotating and a stationary plane disc. This is an idealisation of the situation found in advanced turbo-machinery in which cooling of the rotor faces is necessary. The boundary layer approximations to the equations of fluid motion are integrated by an extension of the numerical technique proposed in Ref. 11. Predictions of drag torque and radial pressure distributions are compared with experimental results from a 30 in (762 mm) diameter system, using a range of speeds up to 4000 rev/min, while varying the axial spacing and rate of imposed radial flow. Qualitative agreement was satisfactory throughout the range, but quantitative discrepancies in the estimates of drag and in the pressure distributions at certain flow conditions suggest that the simple mixing length hypothesis used in this analysis for the turbulent shear terms in the equations of motion is not universally adequate.

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.

Nishihara’s combined bending and torsion out-of-phase fatigue limit data are analysed. The Tresca shear stress failure criterion predicts strengths up to 30 per cent higher than observed. It thus appears that renewed attention should be given to the basic problem of developing reliable combined stress failure criteria. It is suggested that new test methods will be required for this purpose.

This paper presents the flexure functions of some triangular sections, subjected to terminal loads, obtained by using a simple electric analogy technique. The effect on the flexure function of both the shape of the section and Poisson’s ratio of the material has been investigated; examples also include some interesting doubly-connected sections. Flexibility of the analogy technique is indicated.

Experiments in a in (6-35 mm) channel have yielded further information on the precision and convenience of the razor blade technique. It is shown that adhesive tape or carefully located cement can be used to secure a segment of razor blade over a static pressure hole: the resulting calibration for shear stress remains valid if the blade is removed and relocated over the same or a different, similar sized hole. Razor blade segments, calibrated in this manner, have been used to measure wall-shear stress in a turbulent boundary layer with tangential, secondary injection: the results indicate that V. C. Patel’s law of the wall is valid for such flows.

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.

The governing equations for bending of truncated conical shells with multi-layer anisotropic construction are developed by a variational method. The shell is considered to consist of an arbitrary number of alternating soft and hard layers. It is assumed further that the n hard membrane layers are isotropic and may possess different elastic properties, while the (n-1) soft core layers are orthotropic in general and may take transverse shear only. The variations of stresses across the membranes are neglected, as are the surface-parallel stresses in the cores. These assumptions are consistent with those usually employed in single-core sandwich shells. The energy functional is formulated with the stresses considered as independent variables. The stresses are also dependent variables defined in the set of two curvilinear co-ordinates defining the surface of the shell. The stress resultants are introduced as constraint conditions utilising Lagrange multipliers. Successful definition of an elastic neutral surface ensures the uniqueness of shell constants and the equations obtained may be in a form comparable to that of classical shell theory. The system of equations is reduced to a form where Galerkin’s method can be applied directly.

A theoretical study is made of the problem of a long, thick cylindrical tube subjected to two equal and diametrically opposite normal loads. The stress state is analysed by the three-dimensional theory of elasticity, with the Papkovich and Neuber stress-function approach. Numerical results for stresses and radial displacement are obtained to show the nature of stress concentration in the neighbourhood of the load. Some related experiments using the photoelasticity technique are also accomplished. Favourable correlation is shown between the theory and the test results.

Measured characteristics of compressible constant pressure adiabatic turbulent boundary layers are correlated in an incompressible frame of reference with the aid of a modification of the well known Mager compressibility transformation. Quite good data collapse is obtained although the transformation is shown to be deficient in the outer regions of the boundary layer. The results will be used to produce data sheets of constant pressure adiabatic turbulent boundary layer properties.