In a previous note the authors gave a method of solution for the problem of a finite rectangular plate under non-normal loading. The problems considered in the present note are those of constant and variable inclined loading on a circular plate.

The Purpose of this note is to present a table of the receptances of simple epicyclic gears and to show how they may be used. This table of results has two main uses. In the first place the receptances simplify the calculation of the natural frequencies of torsional systems containing these gears by the methods explained previously. Secondly, responses of systems (which incorporate these gears) to given harmonic excitations may be estimated, either in the absence of damping, or when there is damping present of known amount in the component sub-systems. This second use of receptances is illustrated by a simple example in this note; it is based upon the fact that the receptances of a compound system may be built up from those of its sub-systems irrespective of whether there is damping present or not.

A convenient method is pointed out for calculating the response of a damped linear system with one degree of freedom to harmonic excitation. Results of such calculations are usually represented by the familiar “ resonance curves ”—one curve being plotted for each intensity of damping. These curves are not particularly convenient to use and Yates has overcome several of their defects by throwing them into a nomographic form. Yates' nomogram is based upon the concept of viscous damping and it does not give the information of a conventional set of resonance curves in that it relates to the velocity of vibration. By changing over to hysteretic damping, a nomogram of somewhat similar form may be constructed such that it gives amplitudes and phase angles of displacements while retaining the advantages, over resonance curves, of this form of representation.

As pointed out in previous work, in the method of collocation the functions used usually need not be orthogonal or integrable in closed form. Therefore function of different types may be mixed together in representing unknown quantities. Such function may be aptly called hybrid functions. Also, it has been found that usually it is better to represent unknown quantities by similarly looking functions instead of by a series involving higher harmonics. The idea is that by using similar looking functions it is possible to avoid poor regions for collocation, such as near nodal points, and so on, and closer fit in certain regions is assured. Thus if one knows approximately what the function sought looks like, one should try to find a set of function all of which resemble this desired shape, instead of taking an arbitrary set of harmonics when using the method of collocation. Simple examples below illustrate this approach and indicate the good results that can be expected in general.

The problem of bending of thin elastic plates has interested mathematicians and engineers for many years. Various methods have been put forward for determining the approximate solutions among which the variational method of Ritz is most common. This procedure leads to a system of linear simultaneous equations, the solution of which is often quite tedious, although generally by taking a few rows and columns quite accurate results are obtained. The purpose of this note is to show that by using bar eigen-functions for plates which are either clamped, or when some edges are freely supported, certain simplifications can be made in the process and the difficulty of solving simultaneous equations can be avoided; and that the deflection surface of the plate can be derived directly in a series form.

The effect of discontinuities on the analysis of structures is discussed by W. J. Goodey in a Technical Note in the October Journal. He quite rightly points out that a structure with cut-outs is more difficult to analyse (especially for routine calculations) than a structure without cut-outs. Subsequently he indicates a procedure for obviating the former complications by introducing fictitious members in place of the cutouts. Using then the variational method of arbitrary multipliers he derives the stress distribution in the structure with cut-outs from the simpler analysis of the structure without cut-outs.

It is gratifying to learn from Mr. Nicholls (May 1955, p. 364) that he is favourably impressed with the exponential function, and it is to be hoped that he, and others interested in stress-strain relationships, may find it to be of practical value.

While the modifications which he suggests are quite legitimate, they tend to mask the essential simplicity of the function. It would be difficult to obtain the asymptotic stress from his first equation. The second can be easily solved for strain, but the converse process is complicated by the fact that the current stress appears both inside and outside the exponential. It is surely much more straightforward, and infinitely quicker, to plot the stress-strain curve from the proof stress data and analyse it in the normal way.

The Journal in which Mr. W. Tye's Second Barnwell Lecture has been published (“ The Outlook on Airframe Fatigue,” May 1955 Journal) has now reached Australia. I felt that some comment was called for when I discovered that Mr. Tye had not mentioned the work done in Australia on the life of aircraft structures.

What I believe to be the facts are as follows. Australian concern regarding fatigue was awakened in January 1945, when a Stinson air liner VH-UYY crashed with the loss of ten lives. The analysis made by the C.S.I.R. Aeronautical Research Laboratory confirmed that it was caused by a fatigue failure in the welded tube of the primary wing structure.

Mr. H. A. Wills, in charge of structural and metallurgical research at the Laboratory, initiated a programme of fatigue tests on actual aircraft wings, designed to give factual answers to the problem of determining the safe life of aircraft structures. The basic idea that this could be done had been suggested in a paper by Bland and Sandorf0, and the Stinson accident provided the necessary urge.

This note gives the stress distribution in an infinite wedge subject to a general polynomial law of loading along either edge. The method used is that of Complex Potentials, the results of which may be summarised as follows:—

The stress combinations and and the complex displacement are given in terms of two complex potentials Ω(z) and ω(z) by the relations

1

2

3

body forces being assumed absent and pq denoting the stress intensity across a face perpendicular to p and resolved in the direction q, for a body in a state of generalised plane stress, µ is Lamé's constant and k is related to the modified Poisson's ratio σ, by the equation:

.

The paper by Dr. A. H. Chilver (October 1955 Journal) purposed “ to present alternative theoretical approaches to the problem of local instability of a simple type of panel with unflanged stiffeners.”

Examination of these alternative approaches reveals that they are in fact identical and are based on the same approximate representation of the buckled form of the plate by sinusoidally varying lengthwise and transverse deflection, and of the stiffener by sinusoidally varying twist. The difference in the results obtained by Dr. Chilver is explained by the fact that whereas in the first analysis he uses plate theory correctly to express the strain energy in the stiffener, in his second analysis he omits entirely the torsion-bending energy.