The 23rd Main Lecture to be given before a Branch of the Society was held under the auspices of the Merthyr Tydfil Branch on 10th November 1955. The Lecture, entitled “A Review of Some Combustion Problems Associated with the Aero Gas Turbine,” was given by Dr. J. S. Clarke, O.B.E., M.I.Mech.E., F.R.Ae.S. Mr. C. S. Gardner, Past President of the Merthyr Tydfil Branch, opened the proceedings by welcoming the guests. He was deputising for Mr. W. R. Morgan, the Branch President, who had unfortunately had to go into a nursing home for treatment for an old war injury. He apologised also for the absence of Mr. McGibbon who arrived back from America only that day and was unable to be present. He then introduced Mr. N. E. Rowe, President of the Royal Aeronautical Society, whom they were very honoured indeed to have with them. When they thought of the journeyings that his presence involved he thought they should be all the more grateful that he could come and support them in their Branch. He would ask Mr. Rowe to take the Chair.

The most powerful theoretical tool in the solution of the aerodynamic problems of aircraft is the theory of small perturbations, which states that if a wing is thin (or a body slender), and if the incidence is small, then in inviscid flow the fluid velocity at any point can be treated as a small perturbation from the stream velocity. The backbone of our knowledge of the aerodynamics of aircraft is provided by this theory, to which the effects of thick wings and large incidences, and the effect of viscosity, introducing as it does the concept of boundary layers, can be added as additional or correction effects. It is known that at subsonic and again at supersonic speeds, the theory of small perturbations is a linear theory; that is, the assumptions implicit in it lead to a linear partial differential equation for the velocity potential, with linear boundary conditions.

In a recent study of the buckling of pin-ended struts of a certain light-alloy material the author found it necessary to use ball-end fittings which supported rigidly an appreciable length of the strut. For some of the struts—having slenderness ratios of the order of 20—the unsupported length was only about a quarter of the overall length between pinned-ends, (Fig. 1). The effect of rigid end-fittings can easily be taken into account in calculating the elastic buckling load of this system. The author expected to find this end effect important for shorter struts; however, this is not the case. In fact, buckling of the strut is governed largely by the flexibility of the unsupported length, and even large end fittings may not affect appreciably the buckling load.

The twist that arises from bending stresses in straight cantilevers of thin-walled section asymmetrical about any vertical plane, is well known and eventually leads to the concept of a shear centre. If an analysis is made along the same lines as that used for investigating straight beams, of cantilevers curved in plan, it is found that the bending moments transmitted are again responsible for shear stresses in the flanges of the beam and cause twisting.

The following analyses refer, principally, to cases in which the cantilever carries a concentrated load at its end and are confined to the relatively simple forms of the channel and I-section. Each cantilever is perfectly built-in at one end and, for simplicity, it is considered that the web of a section offers no resistance to bending and that the beams are of constant curvature in plan.

Simple Formulae are presented for the first three bending-type and the first torsion-type natural frequencies of any constant thickness cantilever triangular plate. The formulae are derived by a semi-empirical method. Comparison of calculated frequencies with test values indicates agreement within a few per cent. for a variety of plate plan forms.

If the definition that hysteretic damping is proportional to displacement but in phase with velocity be accepted, then the free vibration of a simple oscillator may be treated, without ambiguity, using this concept. The apparent anomaly which Dr. Bishop points out in his paper “ The Treatment of Damping Forces in Vibration Theory ” (November 1955 Journal) arises through confusing three distinct possible mathematical representations of some unspecified vibrating system.