A Numerical Method in the Theory of Vibrating Bodies

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Abstract
In this paper a numerical method is presented for the determination of the characteristic numbers and modes of vibrating (conservative) systems. The method for continuous bodies is based on a finite difference approximation and is a ``relaxation method'' in the same sense as the term is used by R. V. Southwell. No claim is made of theoretical advancement in the subject; the paper purports to present a thoroughly practical method of obtaining numerical answers speedily. Detailed computations are carried out for the transverse vibrations of a quadrangular elastic membrane. The nature of the method is such that it can be easily extended to other vibrating systems of finite or infinite number of degrees of freedom. It is to be emphasized that the quadrangular shape is just a simple example; the real strength of the method lies in the fact that numerical results can be obtained for bodies with more complicated and irregular boundaries.

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