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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(1):63-73; doi:10.1093/qjmam/10.1.63
© 1957 by Oxford University Press
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VIBRATIONS OF BEAMS

I. LONGITUDINAL MODES

G. J. KYNCH and W. A. GREEN

( University College of Wales Aberystwyth )

Second-order perturbation theory, using known solutions for a circular cylinder, is applied to the exact elasticity equations to determine the wavelength frequency curves for the longitudinal vibrations of a non-circular cylinder. General formulae are given and applied to elliptic, square, and rectangular beams. Owing to resonance, the simplest technique is inadequate at certain wavelengths for elliptical and rectangular beams, and this makes the method rather cumbersome. It is also clear that such sections as a square deviate sufficiently from a circle as to demand the inclusion of third-order terms.


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