Tables of Characteristic Functions for Uniform Beams with Sliding Ends

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Abstract
Tables of the characteristic functions of certain types of uniform beams were published by Young and Felgar in 1949. The functions concerned represent (to suitable scales) the principal modes of free flexural vibration, although their uses are far more extensive than is implied by this. Some of the uses to which they can be put are mentioned in Ref. 1 and others are discussed by Felgar and Bishop; they cover both statical and dynamical problems and relate to beams, plates and shells and include problems of elastic instability. In fact these functions can be used in series representations in the same way as circular functions are used in Fourier series. One of the main uses to which these characteristic functions may be put does not appear to have been described in print, although the relevant formulae are quoted in Ref. 2. The functions can be used in vibration analysis to shorten calculations, sometimes leading to very considerable savings of labour.

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