Journal of Mechanical Engineering Science

A method is proposed for dealing with large rectangular and circular tubeplates, in which edge loading and deflection is absorbed by a bellows or a diaphragm. The simple design procedure is based on curves derived from a theory which considers a strip at the edge of the tubeplate. Specimen curves and a recommended design procedure are included.

Reference is made to the ratios known as deflection and ligament efficiencies and results of tests are given which suggest that the values of these are in fact lower than those in general use. In an example it is shown that a significant saving can result by the use of a diaphragm in place of the more conventional bellows. Finally a description is given of a test rig, designed to check the values of stress and deflection in a given system of loading.

This paper is a sequel to a previous work in which the vibrations were considered of a gyroscope mounted on a uniform elastic shaft within two rigid gimbals. The theory has now been extended to include a more general practical arrangement in which the shaft is non-uniform. Experimental results have also been obtained which confirm the general conclusions of the theory.

Equations have been derived which enable a numerical analysis of axisymmetrically loaded shells of revolution to be made. These equations apply equally to small or large deflection shell theory with linear or non-linear stress-strain laws. Numerical results are presented for the case of an elastic-plastic axially loaded corrugated expansion bellows.

The deformations of uniformly loaded, simply supported beams are derived for a simple creep law of the type

where is the secondary creep rate, ρ is the applied stress and n is the creep index. The solution is extended to include a yielding behaviour such that ρ ≥ Y where Y is a yield stress. The deformations are found to be relatively insensitive to the value of n so long as the strain rate is known at a ‘representative stress’ in the beam and the representative stress is less than about 95 per cent of the yield stress. The concept of representative stress is used to estimate useful upper and lower bounds for the deformations of a simply supported beam composed of a material with a complex creep law in which the stress index n is continually increasing with increasing stress.

Similar results for cantilevers and clamped beams suggest that the representative stress concept is useful for the solution of many problems involving deformations under complex creep laws or for problems in which a minimum of creep information can be obtained.

The lateral deflections of circular cylinders with thin walls were recorded during buckling. Ten pick-up points were chosen along a transverse section of the cylinder, and their deflections recorded simultaneously.

The results suggest, within the precision of the measurements made, that buckling starts simultaneously or with a delay not larger than 0·02 sec, in a large region of the transverse section. Sometimes a local buckling wave appears before general collapse, but this wave does not seem to propagate continuously towards the final shape of the buckled surface.

It can also be concluded that, at buckling and after 0·01 or 0·02 sec, the wall tends directly to a stable polyhedral configuration, with a well-determined number of sides. No intermediate stage could be detected.

These results are interpreted according to previous studies of one of the authors, in such a way that an explanation of the ‘jump’ phenomenon is attempted, without the necessity to pass over Tsien's ‘energy jump’.

In studying the performance of laminar bearing films one need give little attention to the details of the internal flow. The velocity distribution is so simply related to the pressure gradient that one is able almost immediately to concentrate on the pressure distribution. But for a turbulent film the situation is quite different. No simple laws are known relating the volume flow through the film to the pressure gradient and relative velocity. A thorough study of the motion within turbulent films must be made before their characteristics as bearing films can be assessed.

Thus this work falls into two parts. In Part I the basic analysis of two-dimensional turbulent channel flows is given. The application of its results to bearing analysis is treated in Part II.

A multiple crack of four arms in an infinite plate in uniform tension is simulated by means of a ‘square’ hole with curved sides. The conformal transformation uses two terms, the decimal coefficient of the second term being determined by a function generator. The stress distribution due to such a discontinuity is obtained theoretically by derived complex potentials, the results being compared with stress values found by photoelasticity.

Stress concentration factors are given for other discontinuities in the form of square and triangular holes, and cracks of three arms.

Good agreement is shown to exist between theoretical and experimental results.

The linearized equations and transfer function for a hydraulic servomechanism are considered. It is shown that the simple first-order equation is inadequate to explain the behaviour of the device as observed experimentally. The solution of the third-order equation, obtainable by the inclusion of the effects of leakage and compressibility, provides a more accurate description of the behaviour.

The theory is extended by means of an analogue computer to include the effects of Coulomb damping and to investigate the behaviour of the system when driven by a harmonic input. It is shown that the stabilizing effects of the Coulomb friction can be simulated by an equivalent viscous friction by increasing the leakage coefficient in the equations. The results of a series of experimental tests are included for comparison.