Vibration characteristics of a linearly tapered cantilever beam and a shaft have been studied by using the lumped inertia force method; a linear displacement distribution is considered over each element. The results are compared with some of those in the literature and with experimental observations. These comparisons indicate that, even using a few elements, a reasonable degree of accuracy can be obtained in the natural frequency, although it is essential to consider more elements in order to determine mode shape accurately.

The supersonic flow past an elliptic cone of small eccentricity is treated as a pertubation of the axially-symmetric conical flow. The perturbation is singular; a uniformly valid solution is constructed by formulating the problem in sphero-conal coordinates (in which the cone surface is always a level surface of one of the coordinates) and by using the method of matched asymptotic expansions. This formulation enables first-order results to be obtained economically. In a numerical example for the flow past a cone of quite large eccentricity at incidence, it is shown that the present first-order solution (of three terms) agrees as well with experiment as a ten-term approximation obtained by Martellucci using the method of linearised characteristics.

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.

The paper presents a solution to the buckling under shear stress of infinitely long plates orthogonally reinforced by stiffeners having both flexural and torsional rigidity. Each family of stiffeners is assumed to consist of equally spaced identical stiffeners. Numerical results are given for the case of a plate with transverse stiffeners and a central longitudinal stiffener for the following three cases:

• (i) Transverse and longitudinal stiffeners of closed tubular cross-section.

• (ii) Transverse stiffeners of closed tubular cross-section, longitudinal stiffeners possessing only flexural rigidity.

• (iii) Transverse stiffeners possessing only flexural rigidity, the longitudinal stiffeners being of closed tubular cross-section.

Relationships between the buckling stress parameter K and the flexural rigidity parameter γ of the stiffeners are presented for each of the three cases when the identical transverse stiffeners are placed at spacings of d, 0·8d and 0·5d, where d is the depth of the webplate.

Case (i) has provided values of the buckling coefficient K for finite rectangular plates clamped on three edges and simply-supported on the remaining edge.

Theoretical and experimental natural frequencies and modal shapes up to the fifth mode of vibration are given for a straight blade of asymmetrical aerofoil cross-section. The theoretical procedure consists essentially of transforming the differential equations of motion into a set of simultaneous first-order equations and solving them by a step-by-step finite difference procedure. The natural frequency values are compared with results obtained by an analytical solution and with standard solutions for certain special cases. Good agreement is shown to exist between the theoretical results for the various methods presented. The equations of motion are dependent upon the coordinates of the axis of the centre of flexure of the beam relative to the centroidal axis. The effect of variations of the centre of flexure coordinates upon the frequencies and modal shapes is shown for a limited range of coordinate values. Comparison is made between the theoretical natural frequencies and modal shapes and corresponding results obtained by experiment.

Measurements of the pitot pressure between the body and shock on a 15° semi-vertex angle, spherically blunted cone were made in the RARDE Hypersonic Gun Tunnel at a Mach number of 8·6. Using these measurements, together with the measured shock shape, the other flow field parameters were calculated. The results were compared with results of inviscid theoretical calculations for a similar cone at a Mach number of 10.

An improved reversed-flow formulation of the Galerkin-Kantorovich-Dorodnitsyn multi-moment integral method is presented in this paper. Convergence and accuracy properties of the approximate solutions of the Stewartson lower branch similar flows are given. The approximate solutions obtained with the new formulation for the lower branch similar flows are, in general, more accurate than those obtained with the classical Pohlhausen method or either of the previous formulations used with the GKD method.