Frequency Analysis of Beam and Girder Floors

A procedure for finding the frequencies and modes of such three-dimensional structures as the floors in boiler houses by utilizing the solutions of the two dimensional vibration problems of all the beams of which the system is built up is developed in this paper. The method is explained for the case of floor systems; but the formulas apply also to any other type of structure as, for example, to multiple-story building frames or to airplanes. The method can be used with advantage for the frequency analysis of any complicated structure, and consists in resolving the system into two simpler systems, the frequencies and modes of which are easier to determine. If necessary, this simplifying process can be used repeatedly. The principle is theoretically exact but leads to the use of infinite series; for practical purposes excellent approximations are obtained by using only the first few terms of these series. A reader who wishes to apply the method should have some knowledge of the theory of oscillations and, in particular, of the fundamental notion of “normal modes” and of their properties.