342 REPORTS ON THE STATE QF SCIENCE, ETC. ’ 
The following problems have been considered, in the belief that they are the 
most important which confront the designer :— j 
I. The calculation of Centrifugal Stresses. 
II. The calculation of Transverse Detlections in Diaphragms and Discs. 
Ul. The calculation of Critical Speeds (or of the Normal Frequencies of 
Free Transverse Vibration) in Diaphragms and Discs. 
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Fic. 16. 
Two types of disc have been considered, as shown in the above figure : type A 
is a disc of uniform thickness, and type Ba disc of which the thickness varies 
as some (negative) power of the radial distance. The fact that theory demands 
an infinite thickness at the axis is not a practical objection, since an actual disc 
is bored to receive a shaft of finite diameter, and allowance for this circumstance 
can be made by means of an auxiliary stress-system. 
Problem I. Caleulation of Centrifugal Stresses in a Dise of Specified Profile. 
The analysis of these stresses, in a disc of uniform thickness, has been worked 
out by C. Chree,? and a discussion of the problem, with an extension to discs 
ot type B, is contained in A. Morley’s Strength of Materials.t_ Recent investi- 
gations indicate that the centrifugal stresses in a disc of any specified profile 
can be determined without much difficulty by means of graphical methods, but 
it is doubtful whether these methods are urgently needed by the designer, who 
will probably be content with analysis which is applicable to discs of type B. 
Strictly speaking, the loading due to the blades will not be distributed 
uniformly along the rim, but will vary from point to point. If the stress-distri- 
bution near the roots of the blades is a matter of practical importance, it will 
be desirable to investigate this auxiliary stress system : the requisite analysis 
should not prove difficult, for since the blades are uniformly spaced, we may 
conveniently analyse the load system, as regards its variation along the circum- 
ference, into Fourier components, and of these it is probable that only two or 
three will be important. 
’ Proc. Camb. Phil. Soc., vol. vii. (1891), part iv. 
“ Chap. xi. 
