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Approximate Methods for Finding Frequencies of Vibration*

Published online by Cambridge University Press:  28 July 2016

J. Morris
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Extract

The rapid progress made in mechanical engineering during the present century has brought many troublesome problems in its wake. One of the most serious of these troubles arises from resonant and such like vibration. It has, therefore, become increasingly necessary for a designer to take account of vibration. A powerful instrument for this purpose was provided by the late Lord Rayleigh, whose method for finding an approximation to the fundamental frequency of vibration of an elastic system is fairly well known. In this paper an attempt is made inter alia to explain Rayleigh's Principle and to clarify, so far as the author is able to do so, the basis of the principle. Other devices for ascertaining approximate frequencies are also given and an appendix has been added on forced vibration experiments.

Type
Research Article
Information
The Aeronautical Journal , Volume 40 , Issue 311 , November 1936 , pp. 815 - 832
Copyright
Copyright © Royal Aeronautical Society 1936

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Footnotes

*

Crown copyright reserved.

References

Note on page 817 * W. Ritz Journ. f.d. reine und angewandte Math. CXXXV, 1 (1908); Gott. Nach. 236 (1908); Ann. d. Physik, XXVIII, 737 (1900)

Note on page 817 † In the usual application of Rayleigh's method for this example the corresponding1 function of the same degree would be

Y=a{x 2—(x 3 / 3l)}

which would satisfy the boundary conditions

x=0, Y=0,dY/dx=0; x=l, dY2/dx2 =0;

This would, however, evidently give a less accurate fundamental than that obtained by the method given.

Note on page 826 * Phil. Trans. A. p. 279 (1894).

Note on page 826 † See ” Strength of Shafts in Vibration.“ Chap. III. J.Morris. (Crosly Lock wood.)

Note on page 827 * This series solution may be readily expressed in terms of Bessel functions, but for the purpose in hand the series form is retained.